A car voltage regulator controls the alternators voltage/current by adjusting the field current to the alternator, your treadmill motor has a fixed field that is the magnets, that is why the car regulator does not work.
As G said you need a simple dump load regulator set at say 14V, with a dump load to suit the output of the treadmill motor, look at the bottom of G's post click on his site link it just happens he can sell you one. For a simple system your battery will work.
allan