28mm tires @ 110 to 120 psi should not be too hard -- particularly if you weigh 220. I'm kind of a fatty being 205, down from about 240, and I run my 28mm tires (Panaracer Pasela TG) at about 110 or so and ride a B17. It's not a problem as far as comfort. My limiting factor, recently, is getting enough hydration in the Houston heat -- it's quite a chore to drink enough liquid to replace the liquid lost (maybe 1.5 oz/ mile). The 28mm tires @110 psi are plenty squishy on any Houston roads, maybe you're running rougher roads. I have one bike with 35mm tires (Schwalbe Marathon Plus) that I run at 100psi. Anything less feels like riding on jello.

Just a thought, if you find that you're putting a lot of weight on your saddle, you might want to try raising the saddle height a bit. Most of your weight should be carried by your legs, not your butt.