Jason, thanks for posting those pics, they are a valuable supplement to the other thread. It looks to me as if the pinion screws onto the pulley shaft - if your second-last picture went up a bit higher we could probably see the end of the shaft and be sure. My method for removing such things is simple but involves you making a tool. The tool spans the two holes in the clutch member that squeezes the clutch material against the pulley. It is apparent that the previous owners have not made a proper tool but have mangled the clutch member a bit with loose pins, probably with threads on them. If you make a tool by taking a piece of, say, 1.25 by 0.25" flat steel about 15" long, drilling a pair of holes the same diameter and distance apart as the holes in the clutch member, and welding two pieces of steel rod through those holes, it should be useful for removing one of the other pulleys on the mower as well, and will not harm the mower, even with repeated use. To hold the gear without damaging it, my method is to squeeze it between two blocks of soft wood, in a vice. The gear teeth will bite into the wood, preventing rotation without harming anything. Then apply your pin-wrench to the clutch member and it should screw out, and later back in, with no fuss. Be careful, because I believe it would require a left-hand thread. The pulley is driven anticlockwise by the belt to move the mower forward, and if it had a right-hand thread in the pinion, it would simply unscrew in service.
I think there is a good chance that the plastic gears usually failed because someone tried to use the gear train to resist the unscrewing of the clutch member, to service the clutch lining. There is only one way that could end, with a plastic ring gear restrained only by moulding it onto a knurled surface on the outside of the hub. However they could also have been broken by people trying to pull them off, instead of dismantling the whole central mechanism of the drum.
