SYMPTOMS: (Inadvertently posted to wrong Board earlier; thanks
to Hendrik for noticing.)
Left rear axle slid in and out on its bearings about 1/2 inch.
(Previously reported as "more than one inch." In my shock and
amazement I apparently exaggerated just a bit.)

PROBLEM:
More than 15 years ago, someone had apparently dissembled
the left rear axle, then reassembled it without installing the
inner spacer (Part No. 47905D). This is what allowed the axle to
slop in and out.

COLLATERAL DAMAGE:
There was so much slop that the bull gear was able to abrade
the inside of the reduction housing unit oil pan, filling it with
metal shavings. Eventually the pan wore through, allowing the
gear oil to drain out. When I bought the tractor, the pan was
dry, with lots of metal filings, and the bull gear teeth were
covered with a thick, gritty grinding paste.

SOLUTION(?):
I disassembled and cleaned the axle shaft, bearings, and bull
gear, and cleaned the inside of the reduction housing unit as
well as I could. I couldn't get at the pinion shaft, but removed
the pinion bearing dust cover. I used Seal All to seal the leaks in
the old pan (oil-proof, but not structural), then reassembled the
axle shaft, filled the pan 3/4 full of kerosene, and reinstalled
that, but left the dust shield off the pinion bearing. Then, with
that wheel off the ground, I ran the transmission in 4th and
Reverse for a couple of minutes each, to spray the kerosene
around inside the housing. The kerosene also sluiced through
the pinion bearing, and ran down the outside of the housing,
into a strategically placed tub. Then I removed the pan, dumped
out the kero, wiped out the metal filings, cleaned off the teeth of
the bull gear, and repeated the procedure. After doing this
routine nine(!) times, there were no more filings, and just a few
sparkles in the kerosene. I then again disassembled and cleaned
the axle shaft, bearings and bull gear, as well as the inside of
the reduction housing, and reassembled everything, using a
replacement oil pan (from Wengers of Myerstown), and filled the
housing with gear oil.
Next year I plan to do the brakes, and at that time will have the
reduction unit housing off, and can give it a good cleaning and
inspect the pinion components. If things don't look too bad I
plan to put in new bearings and seals, and reverse the pinion
and bull gears on their splined shafts so that most future wear
occurs on the less-worn Reverse side of the gear teeth. But if
the pinion is shot and/or the bearing housings have worn too
large, I'll be in the market for a replacement of the complete
reduction unit housing. (Note: I plan to pull the pan of any
replacement to check for oil before buying...)

Thoughts?

--Bruce

Don't think I would reverse gears. If they are worn badly I would replace them. If not worn badly you do more harm than good by reversing them. They are meshing together now and you may cause a whole new wear pattern to develop.

Given the situation you (and the tractor) were in and your planning to tear into it further some time, you did allright. I would not be surprised if the dislocated bull gear also ate some cast iron away from the inside of the final drive casing.
You cannot reverse the bull gear since it is a-symmetric; although one could swap the left and the right bull gear which would basically reverse them. You cannot reverse the pinion since it it part of the differential shaft. I concur with Phil that you should not reverse one member of a worn in pair of gears.
So replace parts as necessary as you tear into it. Replace all seals and bearings (the bearings being standard ball bearings are relatively cheap anyway). Your old seals will be shot, especially after this spell of running with too much axial play.

Ask questions where needed!