Small item to keep in mind: the rear axle limit, no matter what the rating is, will always be the capacity of the 2 rear tires on a SRW truck--and that is normally around 7500 lbs.
Also: to estimate the potential pin (hitch) weight, industry norm is 20% of the GVWR--in your case, this would be 3100lbs--this is why it is important to know BOTH the rating of the rear axle (RAWR) and the actual weight without the trailer on it.
Yes, you would be better served with a 3500/350 SRW pickup to help expand your choices of available fivers.
Another item to consider: the various tank volumes you list at 50/134/52 gal---if you were ever to need to travel with the tanks full that could add almost 2000lbs to the weight of the fiver.
As Jim said, lots of people pull such units with 3/4T trucks--just not a great or safe idea.
Have you seen, or looked at, the following GM publication?
https://www.gmfleet.com/content/dam/...wing-guide.pdf