Sometimes a cord breaks or shifts in the carcass of the tire, which causes exactly what you describe. 

Tires can get flat spots on them when sitting in one place a long time.

New set of Yokohama Advans cured the problem.
Not near as much tractions as the Nitto 555’s though, even though they are advertised as being very sticky. They have 280 tread wear rating and are supposed to be soft for traction.  Ride good and are quiet. Let’s see if I still like them by the time I get to the bash.

6sally6 can show you how to get flat spots off rear tires....I hear Tubo3 can too

Steve,  So, No issue with rack and pinion after new tires?

New tires are fine. No rubbing in rear like old ones, even though same 245x45/17 size. I think my TCP r&p is having an issue with L-R power bias. New tires greatly eliminated the wandering but not 100%.  I bought a borgeson and might swap it out.  Everybody that has borgeson seems to be happy with them.

Agreed on the pressure kit. I have the box on my 68 and am very happy. With caster maxed out the return to center is acceptable. Biggest issue was the number 3 exhaust tube from my JBA headers hitting the top of the box. Percussion engineering fixed it, but I couldn't live with that, so I cut and rerouted the number 3 & 4 tubes to clear the box.

MS wrote:

I have the KRC pump on my car and am using the smallest orifice made to lower the pressure as much as possible.

MS:  Tell me about your steering and KRC pump.  I have the same setup and the steering is way too easy; like the early power steerings.  What have you done to stiffen things?
 

MS wrote:

They make various size orifices for the KRC pump to provide various pressures. Go to Speedway and order the smallest orifice. It take ten minutes to swap it, right where the pressure hose comes out of the pump. You remove the hose, replace the fitting that contains the orifice, then screw the hose back on. Be careful, as the oricice has a spring behind it. Thumb pressure will hold it down.

Thanks, Steve