I assume the loaded bulge is from a front end loader? 24psi seems rather low for a front tire on a loader tractor. The common recommendation is to run the fronts at the maximum sidewall pressure on loaders, which you are currently at with unsatisfactory results.
I would start by confirming you have the correct tires on the machine load-wise, and make sure you're under the tire weight rating. Next, (again, just my opinion) I would try inflating them to maybe 30-40psi and see where you're at.
R1's are going to bulge under load, how much is too much is subjective. I have R4's with much stiffer sidewalls and keep them inflated to max sidewall pressure.