Well yeah... the car's handling characteristics are designed around the stock Super Sports, of course if you go down from a summer performance tire down to an all season, the car will feel different.
Yup, i road trip mine a lot too, just not to your extent. LOL. I've done a trip to San Francisco, Bakersfield multiple times, LA like it's down the street, Las Vegas and down to Actual Mexico in Puerto Nuevo. The car truly is amazing, it's amazing that there is now such things as a BEAUTIFUL car...
Nice! Enjoy her bro! It's an amazing machine minus the little flaws like wind buffeting and whatnot, but those are easily fixable and doesn't take away from the fact that the Supra is an amazing car overall!