Hi all,
I know this was started some time ago, but for anyone's future reference wanted to clarify the reverse gear can be changed without splitting the tractor.
Using the operator's seat as reference, the right side of the bell housing has a clutch inspection/throwout bearing grease fitting access cover held in place with two bolts. With this cover removed, one can use a ratchet with a deep well socket to remove the retaining plate that holds the reverse gear shaft in place. If you have large hands, it is hard to reassemble this way. Removing the steering assembly will also provide access to this retaining plate and in my opinion, is the better way to go as it allows more access and a visual of the plate/bolts.
Remove both shifter covers to expose the gears. At this point you'll be able to see the reverse gear and the apparent damage to the rear of it. Typically wears a groove about 1/4" deep. If you cannot see the gear completely, drain the trans fluid until it is exposed. I recommend completely draining and flushing the system as the shavings from this gear wearing away are now likely throughout the transmission (hopefully caught by the filter). Draining will also give you a good look at the main shaft. If the main shaft is worn, it's probably not worth wasting that new reverse gear as it'll just get chewed up again. Changing the main shaft requires a split.
However, if the main shaft looks ok/acceptable then the shaft for the reverse gear can be pushed forward toward/into the bell housing, allowing enough clearance to slide the bad gear off and a new one on. The shaft is held with an o-ring toward the front so it will not likely slide easily. I used a cheap, long screwdriver that I bent into an "L" shape and pushed the shaft out from the rear. The trans casting is countersunk to hold the shaft in place toward the rear with a through hole of smaller diameter. Insert a tool (in this case, it was my bent screw driver) and apply pressure to extract the shaft forward.
Reassemble in opposite order, make sure to clean out the filter and flush out the cavity prior to refilling with fluid. Then have fun lining all the shift forks back up. I found it easiest to start with the reverse fork and work back toward the PTO forks.
I hope this proves to be helpful to some in the future.
Joel