You should have no more than 36 psi in the front. I run about 34 front and 40 rear for a little more compliance, but that is with the M030 suspension. There should definitely not be any rubber band feeling in the steering with any 996.

 

Update: After driving this car for another month or so, I think the issue with the car might be suspension, or shocks, or bushings. I've never had to replace any of these items on any of my cars in the past, but the car floats over large dips and actually seems to twist - indicating that one of the shocks might be shot or responding differently than the other on the other side...

Other than having someone watch the wheels from another car while driving over large bumps, and other than jumping off the car's bumper (I read that somewhere, lol) to check the shocks, are there any other tricks to determining what's wrong? Two different shops didn't see any issues

 

At almost 20 years old, anything rubber or plastic will begin to fail if not already...

 

There should be a good shop around that has quality tools to measure the shocks, there ain't much to see on shocks, other then if they leak.
I am also picky on alignment shops, I only trust one around here. The others have all the tools, but don't really know what they are doing...
Knowing the quality of roads around Chicago, 50kmiles might have been enough....

 

So I made an appointment at Midwest Performance Cars in Chicago. Here's what they said:

"We've confirmed the floaty and almost unresponsive handling at higher/highway speeds. The tires are in good shape and a good brand (Michelin), no suspension components are faulty, have play or are in need of replacement. Our recommendation would be to upgrade the struts, shocks and springs with either Porsche sport, ROW M030, or KW suspension kits. An alignment would be needed after."

Everything else looks really solid on the car!