Is the variator manually adjusted?
If so you could normally leave the variator in the upper end of its' range and use the VFD to get the spindle speed you want. Just don't run the motor rpms below 20%-25% of the full motor speed or you'll run into motor cooling issues. Below that speed the motor's fan won't be turning fast enough to move enough air to cool the motor.
The only time you'd need to adjust the variator would be if you needed a spindle speed that was above the back gear range, but that spindle speed put the motor speed below the 20-25% of full motor speed. If that happens, then crank the variator into the lower end of its' range. That would allow the VFD to bring the motor rpms up - hopefully high enough to cool the motor.
Of course this all assumes that you'll be running the motor long enough for the heat to build up enough to damage the windings. Or, that you'll be running the motor at this low speed for short periods, but with insufficient time between motor cycles for the heat to dissipate. In that case, the heat could again build up enough to damage the windings.
I installed an a 900HP compressor a few years ago that took over 25 seconds to come up to speed on start-up. It accumulated so much heat in the motor that we weren't allowed to try starting it more than 3 times in a 24 hour period - with at least 1 hour between each start-up attempt.
Don