@CapriRacer do you have any thoughts on this situation?
Yeah, I do.
What is probably driving this is the nylon cap plies in the tires. In order to get rid of the flat spots, the temperature of the tires has to be raised above the "Glass Transition Temperature" of the nylon.
Explanation: Unlike what we have been taught in school, matter is much more complex than just "Solid/Liquid/Gas". Some materials change structure - and nylon is one of them. It's called the Glass Transition Temperature, where the nylon changes structure - and it is driven by temperature. Unfortunately, the temperature where this occurs is only slightly elevated over ambient and tires can reach that temperature fairly easily.
So the fix is to elevate the temperatures, then allow the tires to cool while maintaining the desired shape. That might mean lowering the inflation pressures and operating the tires for a length of time (say 30 minutes), then immediately jacking the car off the ground so the tires are suspended. I can think of a number of ways to do this - like one end at a time.
Unfortunately, Pennsylvania is still not very warm yet, so this might have to wait a few months - and it will take a bit of experimentation to get it right because if the temperatures get too high, the tire could be damaged beyond fixing!
And just a word of warning, I have never seen this done and don't know if it will work, but I think that is the only thing left that stands a chance of working.