tow vehicle tire air pressure/load quandary

I have to replace tires on my Trailblazer soon, which I use to tow 5000 lbs (with no problems in over 25000 miles), with load leveling, anti-sway. The current tires are Toyo Open Country P245/65R17 with a load-speed rating of 105H. The tires are rated full load of 2039 lbs @ 35 psi (stamped on tire). The placard on the Trailblazer door recommends 32psi front and 35 psi rear. So I typically pump them up as per Chevroet's recommendations. This is where I get confused!! When you look at the tire with the trailer hooked up, you can see an increase in sidewall bulge. I was thinking if I got a tire that could handle a higher pressure, I could have less bulge, and better gas mileage. For example, a Goodyear Assurance CS Fuel Max is rated 2149 lbs at 51 psi. So what does this all mean? I buy tires that can take more pressure, and pump them up until the bulge is the same as when I am not hooked up to the trailer? What happens then when I am driving about with say 45 psi in the rear tires, 10 lbs pressure above what Chevrolet determined was appropriate for this vehicle. Is that bad? Good? Don't matter?