Also, you can run your simulation on integer math that does have deterministic results. Incidentally it's probably how the universe works too. Quantum physics specifies that units (quanta) are not infinitely divisible. Even frequency of light shouldn't be infinitely divisible if you consider the quanta of time to be the speed of light over the planck length.
All you need to do is send definite updates on object locations frequently enough that the error is not significant enough to be noticeable by players. In network game play the overriding error problems stem from network lag rather than FP divergence. For the most part it does not matter that your player is .001 millimeter from where they should be.
Everyone who has sniped in Team Fortress knows that you have to lead your target a little for 'lag'. Ostensibly this is because the bullet takes time to travel, but realistically probably stems from lag.
In all honesty just write the game using whatever running on whatever and if it looks realistic it's probably good enough. If you really can't solve the problem find a guy in creative to augment your story line to match the weirdness in your physics simulation.