The movement of the floor is your big problem, and you already have
several good suggestions. But I would ask if the floor joists are
accessible? For instance is there a basement under this floor? If so,
is there bridging for these joists? Just another thing that might help.

There is an unfinished basement underneath and all the joists are
accessible. There are 2" pieces of wood forming "X" braces in a row the
whole length of the house. A couple of them are split where the nail is,
but they don't move if I push and pull on them.

Thanks
Dante