I believe cheating is not necessary to win a match, or even to win most matches. I believe cheating in the way you have defined it is necessary to win Nationals in adult or mixed leagues. Mostly because, the way you defined it, it is impossible to accurately police. So, here's my idea. It's no longer cheating. You can self rate however you want. Once rated manage your rating until your hearts content. Once everyone is doing it, it's no longer cheating. No three strikes. No visual rating defaults. No filing grievances. That's the road to Nationals.
Meanwhile have other leagues that top out at local playoffs. They have a code for ratings and such, just like today's leagues. Winner gets a banner that says something like "Nor Cal Lower Pennisula Women's 2.5 champs." Make it suitable to hang on their courts. I suspect, without the glory of Nationals, the people who will do anything for a National championship will shun this league, leaving it for the folks looking for friendly play against like minded folks that actually play that level. There will be lots more champions. I also suspect there will be lots more players. (Note, if I see people cheating to get a banner, I'd say drop the playoffs altogether.)
Now, for the folks that like to play people from around the country organize weekend tournaments for teams, say a 3.5 team tournament. Teams from all around the country come. The way you get in, your team gets the most votes from teams you've played against. That's right, think of it as "Miss Congeniality" based tournies. I guarantee the cheaters won't make it to this one.