Just an update. I was on the verge of dumping this machine. Oh, it started great, and ran great. But the wheel lock-up when pulling in reverse was unforgivable. I still think Honda is grossly negligent on this design of the drive system.
Back in early June I installed the needle bearings and JB-welded the inside seals, as recommended by Briantii. At the time, the outside seals - felt or silicone rings, had not been suggested, so I didn't do those.
Also, I am a mulcher. I think there is a tendency for clippings to be thrashing about under the deck for a longer period of time, compared to bagging, which will contribute to more debris getting into the drive axle areas. I live in Minnesota, so our mowing season is winding down.
So far, there has been no change in force required to pull in reverse. I am delighted in the results. I won't be disappointed if I have to clean and re-grease after a season's worth of mowing. That sure as heck beats having to do it after every 2 or 3 mowings.
Thanks to Briantii and everyone for their suggestions and observations.