How bout NEVER !
What you have is a mild race engine used as a street rod engine....(I'm proud of you BTW!!)
224 duration in a 289 is considered pretty 'rad' !  (see my above comment!)
A carb is just a controlled 'gas-leak' (BB referred to them as a 'dripping pot'!)
Your fuel system prolly is a typical 1966 style 'open system' meaning the fuel 'vapors' are NOT routed back to the tank
                                                                                                                                   (like a modern fuel injected system)
To get the carb adjusted as near perfect as possible you could weld in TWO bungs in those GREAT long tubes and buy an air flow meter (not the real name) and get the mixture near perfect. (still gonna smell the stinky modern gasoline)
They make a 'perfume' you can mix into the fuel (no kidd'in) cherry is my favorite...grape is cool too..(nitro smell is available!)
You got 'yo-self' a skreet-rod pardner!...
You DO have the exhaust exiting the REAR valance don't you?! (very important)
Insure ALL little holes and cracks are sealed up to keep smell OUT of the cabin. (in 1966 there were PLENTY!)
AC would prolly help too. (you're from TEXAS so that's a given...)
I would LOVEto take-a-ride in that 'pony BTW
Other-than switching to FI and a bunch of other mods (listed above) I suggest you 'enjoy-the-machine' ! 
I believe BITD (when all the mods you have listed) you woulda-had a "killer" street/strip rod. The only difference was..back then the gasoline was 100 octane pure gas and smelled REALLY GOOD ...so we didn't complain about the stink.
You could carry a 'clean shirt' wrapped in a plastic bag...and change when you get outta the ride !!
6sally6

6sally6 
Thanks for your reply ,,!!  
                         I needed a  good  laugh !!
                                                     I will consider you thoughtful suggestions..

PS.. your right back in 1974"  my "65"  289 mustang build had a 305 / 460 lift cam ..it didn't smell like gas , I loved the way it loped at idle,. and run 13tens in quarter with a c4 auto 2.80gears ...

maybe the way to go would be to change the cam ??
 

Do you have a vacuum advance distributor?  It would likely idle better and a little cleaner with 20 to 22 degrees at idle.  You may need to recurve the distributor and/or change the stops to give you more initial timing or if you have vacuum advance, connect it to full manifold vacuum.  You may be able to lean out the idle once it has more timing.

How does the oil on your dipstick smell?  If it smells like fuel, the diaphragm in your fuel pump may be leaking fuel into the crankcase.  In my experience that will definitely cause a gasoline odor to be present.

If my car ran great, the plugs looked good, I could find no fuel leaks, but it smelled like gasoline, I would count my blessings, have a cigar and enjoy the day.

Carb bowls have vents, and there's always some fuel in the crab/manifold even when its not running.  I think we've just become hyper sensitive to the smell because EFI cars don't.  

TKOPerformance wrote:

I think we've just become hyper sensitive to the smell because EFI cars don't.  

X-2
6s6
(Although....gas DOESN'T smell as good as it once did...)