You are correct. This topic isn't new. If you search you will find many, many threads. You probably want to read as many prior threads as you can so you can mull on the advice and see what makes sense to you.
I'm guessing the difference in axle ratings comes from the OEM tire ratings. I think you can safely go higher.
Like so many truck campers, your set-up is pushing or exceeding payload limits. You will find much advice about air bags with folks recommending high and low pressures. I always ran ours about 80 psi. You have to experiment to find what works for you.
You are correct that your tires are the weak link. A lot of folks with single rear wheel (SRW) trucks go for 19.5 tires and rims. We did. If I had to do it over again, I would probably try the tires rated at 3750 pounds. Moderation, moderation. The 19.5's drove like rocks unloaded. Good luck.