Wow, lots of complicated suggestions. I don't know the answer. The base question here seems to be whether there should be a 65 game rule for season awards. Then it got conflated into a question about load management in general (or so it seems).
There are not that many players in the league that are legitimately contenders for MVP. I don't really like the rule as it applies to MVP (or other awards). If a player gets injured and misses 20 games, that should be a factor but I don't like the hard cut off. Play 66 games and you are OK but only 64 and you don't qualify?
I believe that a first place vote is 10 points, second is 7 and so on. Maybe make it that if you play less than 65 games, then your first place vote is only worth 9 points, second only 6 points or something. That way it is still a factor but not all in or all out.
As far as load management, so long as there are back to back games, all teams are going to rest some players. Eliminate back to back games and there would be less of this. Some players need rest along the way or they won't get through the season. I don't see this as a major problem and also no realistic way to change it.