I think you've got a hard problem, that's only going to be solved by local expertise.
Trying to 'fix' this sort of problem, from a distance is not smart on our part, and if you do get advice from here, you should take it with a grain of salt. After all, none of us have seen it.
My personal reaction is that I'd probably be doing what your first company did, unless I could see that you had a LOT of spare cash lying around, and wear willing to throw it at the pool. Companies go bankrupt on pool situations like yours.
There are techniques, mostly used in Florida, for installing pools in swamp situations like yours. But they depend on sandy soil to work. And even then, a builder needs to have experience with them, which I do not have.
I'm going to go ahead and put this thread out there -- but I'd caution you to evaluate the responses you get carefully.
Ben
PS: pool "pressure relief valves" -- really, "hydrostatic valves" work on rigid bottom (ie concrete) pools and are useless on vinyl pool. . . . not that that prevents some liner pool builders from using them. They wouldn't help much in your case, anyhow.
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