Complete guesswork here (without seeing your controller board - but you're suggesting some local controller, likely a microcontroller GRBL - complete guess, like I say), IF (guesswork again) the limit switches are couple to the ucontroller discrete inputs then you might be suffering with the intrinsic high-z inputs from the uC device with internal pull-up or pull-downs.

Are the microswitches wired to 0V/Ground? If so, is the switched input (the non-ground wire) floating at around 5V?, if so then you could try reducing the internal pull-up resistance by wiring a 1k resistor from the microswitch input to a local 5V pin. The point here to provide a low impedance path for noise introduced from the spindle to clamp onto the supply lines - by default the high-impedance input to the microcontroller is highly sensitive to signal voltage (and therefore induced noise)... If that makes sense?

If there's any joy with this a more practical solution would be to introduce opto-couplers on the input to the controller - they'd provide good noise immunity.

EDIT:

Can you provide any details of the controller card?, even a picture?