15's won't work without modifying the calipers. 16" rims are really the smallest setup without modifying your car. Someone did it on the 8th gen, but they took a grinder to their calipers to shave them down, and it was a special drag wheel setup.
You could go easily to 16s and buy some comfort tires vs performance. The Si comes with semi performance tires and they definitely give you a stiffer ride. I use 16s for winters and they fit with no issues.
Another option is to sell the Si and get a more comfort oriented car The Si is not the most luxurious or comfort oriented car out there.