I would NOT run the car with the regulator plugged in until you run down the problem.
Problem could be "just grease," it could be a bad regulator, or it could be something wrong in the alternator brushes circuit.
Somewhere buried in the shop manuals is the amount of current that the field circuit draws. If you have a multimeter with a 10 or 20A scale, you can disconnect the regulator wires, and hook your meter in series with the two disconnected wires, the meter set for hi current scale.
My recollection is the field should draw (key on) about 3 amps.
If that seems measurement is OK, I'd go ahead and replace the regulator