Aaron, whatever the cause of your rib injury, I doubt it was from the seat being “too tight” as you state. The rib injury likely is from the g-force of cornering. You will experience exactly the same g-force no matter how tight the seat is. In fact, if your seat is too loose you will be thrown back and forth between the seat sides, increasing the stress on your ribs.
The Tillet seat you have is very good. I switched from one to a Ribtec for reasons unrelated to rib stress and the Ribtec was not a big improvement in that regard. To the extent there was an improvement, it was because the Ribtec was a special “tall” model and at 6’2″ the extra seat hight has been helpful to me. I doubt switching seats will help so long as the one you have is snug.
In my limited experience rib bruising and cracking is the result of pressure points, where the cornering stress is focused on too small an area of the ribs rather than being distributed over the entire side of the rib cage. In my case, an off-brand rib vest created a pressure point because it was too short. Switching to a ribtec vest made the problem go away.