While I don't suffer with a bad back (though I cant be the only one whose 350Z seats give them back ache!), I made the swap from 45 profile on 18's (GT4 alloys) to 35 profiles on 19's (LMGT4s), then back again, then to a 40 profile on 18's (Work T7R's).
The 35 on 19" was a bit too jarring and uncomfortable for me. It made the steering feel heavy and the car generally felt like it was more effort to drive.
Switching back to the 45 on 18 (stock GT4 wheels), car felt more nimble and much smoother however the change in width from my 8.5 front and 9.5 rear LMGT4's was noticeable and the car felt less planted.
Ended up settling on a set of Work T7R's with a 40 profile but 8.5 front and 9.5 rear widths. Really happy with this, Feels more nimble than 19" alloys while still feeling planted and not as crashy.
Also to note is that some tyres have stiffer sidewalls than others which will make the ride firmer, even between two tyres with the same profile.
Normal summer tyres will be softer than 'performance' type tyres, and trackday like / full trackday tyres being stiffer still.