I don't have a JD, but when I did my 150 service on my NH TC25D, it included greasing every zirk in sight, as did the 50 hour service (which my dealer did)! /forums/images/graemlins/smile.gif This was made much easier by having the mmm off. I could lay under the tractor (it sits high enough off the ground that I don't need stands or ramps) and look for, clean off and then grease all the zirks. There were zirks on the front drive shaft, the brake and clutch pivot points, etc., which were covered with just enough dirt that they were rendered invisible.
Without the mmm, I had enough room to actually have the manual with me under the tractor! I'd look at the manual to see where a zirk was supposed to be, find it, clean it off, grease it and see that the new grease was coming out of the fitting, then clean it off again.
My advice? Take the mmm off. It will make the job much easier and, as you surmised, you don't want to get oil on the mmm belts, pullies, etc.
BTW, having a cordless grease gun (Lincoln) also made this job much easier. No need to connect the hose (some zirks were not reachable with a fixed nozzle) from the grease gun and then hope it stays on while you use 2 hands to pump a standard grease gun. Just connect to the zirk with one hand and pull the trigger with the other. Alternatively, no need to use one hand to hold the nozzle on, find a place on the tractor to support the grease gun then use the other hand to press the lever.