Honestly, to get to 40 psi tire pressure at your weight you’d need nearly 2 inch tires. The other problem you’ll have at 40 psi on anything narrower is going to be with rolling resistance. It goes up significantly as you get to those kinds of pressures.

But you are looking for comfort in all the wrong places. Your problem has more to do with technique than equipment. We call the seat on a bicycle “a saddle” for a reason. Like a saddle on a horse, it is there to support you but it is not something that you sit on like a chair. If you sit on it with all your weight, it becomes uncomfortable very quickly. Impacts from the road go straight up the frame to your delicate nether regions.

What you should be doing is using your legs to hold you above the slightly above the saddle. You are in contact with the saddle but you aren’t putting your entire weight on the saddle like you would if it were a stationary chair. It requires a bit more from your core muscles to do this but you’ll find that you glide across things you would have just thumped before.

I regularly ride bikes that are as stiff or stiffer than you Trek with narrower, higher pressure tires (for better rolling resistance) and using harder saddles than you are using. Most of my road bikes have Brooks saddles that are unpadded and are hard, stiff leather. My Brooks aren’t broken down and soft either...they show not dents at the sit ones with tens of thousands of miles on them. But I do ride in a much more dynamic way without “sitting” on the saddle.

I do have bikes where I run 40 psi but those are mountain bikes ridden in even more demanding conditions. I still ride them while hovering over the saddle.