Do you have approximate tire diameters front and back?  I have an idea but need some details like diameter so I can calculate the front and rear wheel frequencies based on the stagger.  Also, have you had a chance to count the rate or period of the rise and fall of the vibration?   Is it constant or does it rise and fall with time.  I would need a number when holding the speed constant.  You have changed all forcing frequencies over time if I follow your posts but the one constant is that it starts at 72.  I wasn't able to follow if it starts at 72 and gets worse with increasing speed or if it stays about the same from 72 on up.  An audio recording would really help.

Numerous sets of wheels and tires, some staggered, some not. Vibe comes on at 72 and does not seem to change frequency as speed increases, even up to 100 mph.
Tires now are 225 x 45/17 ft and 245 x 45/17 rear. Frequency did not seem to vary with any of the various rear ratios or transmissions, even the c4

My WAG ... the only thing in common with its various incarnations, is the body.
The constant of 72 Mph only has wind speed as a factor.
A dyno would rule out mechanical versus environment .... I'm guessing it won't make the noise.

Ever run it with a stock hood? Are the fender braces in place?
I would get some of the magnets that are used on dial indicator stands and attach them at various places, and try to modify the sound or the speed it appears at.

Just my WAG, and worth what you paid for it.

This may sound crazy, but I had a 79 Ford pickup that had about a 3/4" thick oval steel plate about 4 x 18"  bolted to the inside of the cab behind the seat.  I asked the previous owner about it and he said it was a vibration damper installed by the  Ford dealer.  When he bought the truck new, it had a vibration and they installed this to fix the vibration.    It was something from the body causing the vibration. It was a smooth riding truck when I owned it so it must have worked. Not sure if this helps you but maybe there is something other than the drivetrain causing the problem. 
 

Doesn't sound crazy to me. That has been my guess all along. The magic is determining where to put the dampener. Sounds like a job for Gary.

Without knowing the exact frequency that is rearing its head, it is difficult to diagnose from afar (Taiwan this week) without touching, feeling, hearing and measuring.  From a few sites, the approximate tire diameters,relating to revolutions per mile, are about 25 and 25.7".  At 72 MPH, the stagger and therefore the frequency difference between the front and rear tires is 27 cycles per minute.  So, with even small residual unbalance of the combination of the wheels, tires, and rotors, if that was the problem, you would feel this rise and fall at a rate of 27 times per minute rather than 83 as reported by Steve.  I am not eliminating this yet, however.  The actual rotational speeds and therefore the frequency produced by unbalance is approximately 15.5 Hz/960 CPM which is something that you would feel but not necessarily hear.  If this is near one of the natural frequencies of the volume of air inside the cabin, you may feel it in your ears as a pressure pulsation rather than a sound.

So, I need to work forward through the drivetrain.  I know that there are 3.70 gears but if the problem is worse in 5th gear rather than 4th gear, what is the 5th gear ratio of your TKO?  I can't remember if you have the wide or close-ratio version.  From that I can continue the spreadsheet to compute engine speed, firing frequency, and look for combinations that could produce an effect felt at 83 times per minute.

When you hear or feel something increasing and decreasing in amplitude it can be a "beat" caused by two sources at nearly  the same frequency going in and out of phase or amplitude modulation where a higher frequency is modulated by a lower frequency.  The sensation is nearly the same but the cause is very different. I need to map out all vibration sources to see if there is a match.

The various masses being described attached to various areas of vehicles are called tuned absorbers or tuned dampers.  They are designed to kill undesirable vibration at a specific frequency.  For example, the back end of the transmission may have a natural frequency excited by the driveshaft at exactly 60 MPH.  It would be impossible to eliminate driveshaft vibration forces entirely so instead they design a mass/spring system that has the same exact natural frequency as the problem.  So, at 60 MPH, the transmission will be smooth but the vibration absorber will be going crazy to essential counter the transmission motion.  The absorbers effectively split the natural frequency into two separate natural frequencies that have lower response.  You will see these on transmissions, rear ends, even donuts on some driveshafts, and maybe even a little beam witth a washer welded to it mounted on the firewall to kill a sound or vibration at a certain speed.  They are not necessarily transferable from one car to the next.

What is somewhat confusing is this is not a problem that is only at 72 - it is something that appears at 72 and continues with increasing speed.  This indicates that it is not likely a resonance issue but a forced response issue.

So - another test.  If at 72 MPH the beat is about 83 what is it at 80?  Is it still 83 or does it increase or decrease?

It will be interesting to see what happens on the dyno but I suspect it won't show the symptoms because the car is not being "loaded" the same way as on the road.  But never say never.

I'm fighting jet lag and instructor's fatigue so please forgive a few typos.

GPatrick wrote:

Without knowing the exact frequency that is rearing its head, it is difficult to diagnose from afar (Taiwan this week) without touching, feeling, hearing and measuring.  From a few sites, the approximate tire diameters,relating to revolutions per mile, are about 25 and 25.7".  At 72 MPH, the stagger and therefore the frequency difference between the front and rear tires is 27 cycles per minute.  So, with even small residual unbalance of the combination of the wheels, tires, and rotors, if that was the problem, you would feel this rise and fall at a rate of 27 times per minute rather than 83 as reported by Steve.  I am not eliminating this yet, however.  The actual rotational speeds and therefore the frequency produced by unbalance is approximately 15.5 Hz/960 CPM which is something that you would feel but not necessarily hear.  If this is near one of the natural frequencies of the volume of air inside the cabin, you may feel it in your ears as a pressure pulsation rather than a sound.

So, I need to work forward through the drivetrain.  I know that there are 3.70 gears but if the problem is worse in 5th gear rather than 4th gear, what is the 5th gear ratio of your TKO?  I can't remember if you have the wide or close-ratio version.  From that I can continue the spreadsheet to compute engine speed, firing frequency, and look for combinations that could produce an effect felt at 83 times per minute.

When you hear or feel something increasing and decreasing in amplitude it can be a "beat" caused by two sources at nearly  the same frequency going in and out of phase or amplitude modulation where a higher frequency is modulated by a lower frequency.  The sensation is nearly the same but the cause is very different. I need to map out all vibration sources to see if there is a match.

The various masses being described attached to various areas of vehicles are called tuned absorbers or tuned dampers.  They are designed to kill undesirable vibration at a specific frequency.  For example, the back end of the transmission may have a natural frequency excited by the driveshaft at exactly 60 MPH.  It would be impossible to eliminate driveshaft vibration forces entirely so instead they design a mass/spring system that has the same exact natural frequency as the problem.  So, at 60 MPH, the transmission will be smooth but the vibration absorber will be going crazy to essential counter the transmission motion.  The absorbers effectively split the natural frequency into two separate natural frequencies that have lower response.  You will see these on transmissions, rear ends, even donuts on some driveshafts, and maybe even a little beam witth a washer welded to it mounted on the firewall to kill a sound or vibration at a certain speed.  They are not necessarily transferable from one car to the next.

What is somewhat confusing is this is not a problem that is only at 72 - it is something that appears at 72 and continues with increasing speed.  This indicates that it is not likely a resonance issue but a forced response issue.

So - another test.  If at 72 MPH the beat is about 83 what is it at 80?  Is it still 83 or does it increase or decrease?

It will be interesting to see what happens on the dyno but I suspect it won't show the symptoms because the car is not being "loaded" the same way as on the road.  But never say never.

I'm fighting jet lag and instructor's fatigue so please forgive a few typos.

Beat goes on at about the same rate when speed is increased, on up to over 100 MPH.

I have discounted the wheels/tires being the problem because there have been numerous different sets of wheels and tires on the car with same vibration.

Trans in 5th gear has .68 ratio, but it did the same thing with a stock C-4 automatic as well as the T5 that had 0.67 ratio.

Might try weights on the exhaust or wooden wedges crammed in there just to see if it changes anything.  Or a set of noise canceling ear muffs.

Any chance you have aftermarket e-brake cables? I ask because I had a similar vibration occur on my car once. It was a constant sound, started at 45 mph but remained constant at any speeds above that. Pushing the clutch in eliminated the sound, and driving in any gear at varying speeds and rpms did not change when it started thumping. Turned out that the Lokar e-brake cable, which was approximately an inch away from the driveshaft, contacted the driveshaft and thumped off of it at a constant rate at speeds above 45 mph (through some wizardry I've never been able to figure out). Zip tied it up closer to the body and have never had an issue with it since.
 

Not to muddy the water (hey, I'm in Central Texas where we've had plenty) but when I first read this posting, the initial thought is thats just what my Ford Edge does when I roll down my back windows at speed.  The frequency stays the same, it just gets louder with speed.  The owners manual calls it "wind buffeting".  It helps a bit when I slightly open the front windows.
What is happening is the windows sort of act like a pipe organ pipe or a whistle.  Air blowing past an opening initiates a low pressure area which attempts to recover by pulling air back in.
Its pretty darn close to the same frequency as you describe.

Here's another thought:  at 80mph and clutch in (smooth, right?), rev the motor to the same rpms for that
speed  as if the clutch were out.   Just grasping at straws here to determine SOMETHING.