I don't think that solves the problem. Whatever fixed stack size you choose, you still cannot write a program that determines the size of the lists at runtime. A Turing complete system would have to be able to do that.

The only way I see is to allocate (almost) the entire machine memory to the stack, create one giant array in that chunk of memory and then put all lists in that single array. That's tantamount to reimplementing malloc on the stack.