I also continue to think that Putin’s talk about wanting Russia to join NATO was sincere. Yes, that was partly so Russia would have a veto over NATO expansion and other actions, but wouldn’t this have been the best solution?

Do you mean that Russia would not have backed separatist claims in Georgia, Ukraine, and Moldova if they held a veto power in NATO for new membership? This assumes that Putin had no plans for expansion, but I don't believe that's true.