When I was researching tyres, I noticed the Uniroyal Rainsport 3 had a soft sidewall compared to other tyres and because of that gave a comfortable ride.
So just a thought, cheaper than PX'ing for another car
The other thing is to buy wider tyres, so the sidewall height is more, ie, 235 instead of 225,
Or even go up to 45 profile, might spoil the looks a bit and throw the speedo reading out a bit ,but if it helps your back....
I'm assuming you're on 18" wheels