As a few people have mentioned, the design of the shaft, bushing and gear system for the self propelled system on the later model Honda mowers is not great but it doesn't mean that it is bad either. There may have definitely been something defective with your mower from the get-go, and if nothing can be done to permanently fix the issue, then it is time to move on. As with all consumer products, your experience speaks for you only. Others may have similar experiences, but in this case there are likely many more that their's is nothing like yours. Despite your unfortunate luck with the HRR, Honda does make a good product. Reading the horror story that you have so nicely illustrated, I would still buy another Honda mower. Why? Because nearly 15 years of owning Honda mowers and have never had a problem.
Go out an buy a new Toro Super Recycler WITH the Honda engine. Your experience with Honda and their "poor engineering" has to do with their drive train, and not so much their engines. The GCV160 is plenty powerful, quiet and fuel efficient. Plenty of options out there my friend but this alternative would be a good one.