Thank you for the link Gator, that's along the lines of my thinking.
While I still have serious doubts about the basement lifting from the water pressure when there will be no place for water to build up, I have considered creating a bell at the bottom of the footings and wall. It would be simple enough to hand dig out the bottom of the walls to create the bell, it wouldn't matter to the rubber liner, and the additional expense in concrete would be acceptable. This also has me wondering about friction of the walls holding the basement in place. In all the links I looked at about basements and swimming pools that have come out of the ground, they where all held in place by gravity. Not factoring in how much water was in the gravel or sand or fill soil around them, the common factor besides allowing that water in there is that none of them where held in place. I think that a poured wall that uses the dirt as the outside form will also hold that foundation in place. Thinking this through, it would appear to support my idea.
My thought on getting the liner to work is pretty straight forward. It comes in widths of 15 feet and as long as you could want it. I would buy one length 15 feet wide and 40 feet long. I would lay that section across the bottom of the hole and up the walls with the extra laying on the ground outside the hole. then I would get two pieces 15 foot wide by 20 feet long for the other two sides. There are several solvents or specialty glues out there that have lifetime warranties. With over a foot of overlap, I would form the liner along the other side, then glue it together. I've done this with koi ponds and it's a pain in the but to work with, but on a sunny day, it becomes very pliable and fairly easy to mold into place.
I will pour the floor first and let the weight of the concrete pull the liner down into position. Then after tying all the rebar together, I will build the interior forms and then fill with concrete. None of this sounds very difficult, I just have to take my time to get it right.
I like the idea of a backup in case of failure. It would be pretty simple to dig a hole into the floor area off to an out of the way corner big enough for a basin for a sump pump. That will take a little more effort to get the liner to fit into there, but like anything, I'll just stick with it until I get it done. I will fill the basin with sand and form it out so concrete does not cover it up, then install a cover over it. If I find there to be a leak into the liner, this will be the lowest spot of the liner and where the water will accumulate. If that happens, then all I will have to do is buy a sump pump. I will have power in the room, but might also look into a 12volt backup system in case the power fails during an extreme storm. This could easily be located under the stairs.