The new GM is absolutely in charge of the new game. If you want to talk with them privately outside of the game or if they come to you for advice, great, but at gametime you need to play your character and live within the confines of the game as it is. If you've got any tips for getting the new GM over the learning curve, offer to share them.
For coping mechanisms, try these ideas:
Mechanics Assistant GM
If you want to offer your services as a game-time rules resource, that might work. You could speed up the game for everyone by providing rulings when called on to do so if it's in your favorite system. Or you could man the rule books and be the designated lookup guy. It taps your strengths and helps the game as a whole. I wouldn't do that without checking with your GM first, though.
Enjoy the Opportunity
Here's your chance to be a model player and show the other players how you would like players to act at your table. What did your players do that annoyed you? Don't do that. Pay attention. Ask clarifying questions without sinking into game-stalling details. Remember how you didn't like your players checking their cell phones every 5 minutes? Don't be that player.
Quick Notes Are Your Friends
If you get ideas during the game, scribble them down and deal with them later. If you have ideas for a series of How To GM a Game articles, note them and get back to the game. After the game, feel free to draft a setting book for the next game you want to run, but it shouldn't come up during play of your current game.
Know When to Walk Away
If your ideas start getting in the way of the current game, like if you can't pay attention to the game because you're scribbling future game ideas, maybe playing isn't where you should be spending your time. Some people have a hard time "only" playing after GMing. They're different skillsets, and the focus on different things. If you think that the current game is a waste of time, you've got 3 choices:
1. Try to improve it by talking to your GM.
2. Find a different game. Sounds like this one isn't a viable option for you.
3. Stop playing and let yourself create your next game in peace.
For your next game, maybe one-shot adventures will work better for you. Less prep work, and a decent dungeon crawl can last a few game sessions.
An aside: I've managed to avoid GM burnout by giving my players a bigger piece of the plot pie. Let them take control of what happens next a little more. But that's another topic entirely.