Marilynn,
If you use that synthetic grease your Singer motors will not be getting lubed. They are designed to use a grease that softens and flows. Since the synthetic grease does not do that it will not flow down the wick and get to the bearings.
It might work for a while if you put it directly on the bearings, but eventually even synthetic grease gives up and you'll either have to tear down the motors for a relube, or buy new new motors.
For gears it's not a problem so long as the chemical make up of the grease does not degrade the plastic the gears are made from.
Joe