If you need both directions, then all you need to safely control the spindle, is another way of switching the power (a relay is the easiest option) going to the spindle board relay (C terminal).
Connect the FWD contactor coil (after it's passed through the rev part of the contactor) to the NO terminal on the spindle board, and the Rev coil to the NC terminal (again after it's passed through the fwd part of the contactor). Then you have the other relay switching the power to the C terminal on the spindle board.
That way the direction signal to the Spindle board controls the direction (it switches the relay on the spindle board), the step signal provides the 0-10V analogue out to control the speed via the Gemini, and the extra relay switches everything on and off.