CapriRacer... no need to apologize, your opinion is worth just as much as mine.
I agree on the confusing. Hard for everyone, to keep up on the new ratings of various TV tires. The OPs tires are called light truck for 1/2 T trucks/heavy SUVs, but not designated LT in that size. I was wrong to suggest to Jim, that they are LTs, and he is knowledgeable enough to know that. He has real world experience, and stays current, concerning tires, making him, IMO, a top source of tire info, on this forum. Now add in towing large trailers, which you can only learn from experience, what works the best. Using your example, the 44 psi will LIKELY work best, even if max load may begin at a slightly less psi. Like I suggested much earlier, if you could borrow a TT with 1K+ TW, hooked up to a modern 1/2 ton, you could try it, come back, tell us what you learned.
Didn't mean to seem condescending earlier in the thread, but did not want the OP to take advice of towing that heavy, with low door sticker inflation. He was wanting to know if his tires were adequate, and the answer is yes, with proper inflation. More psi will make his towing experience better, especially in the rear. After 6 pages of opinions, I hope he sees this is by far the most popular opinion, of experienced towers, that posted in this thread.
Jerry