When playing a community made map using the new DLC, I can still save my progress using F6, but I can't figure out how to load the resulting save. Am I missing something obvious?

The load key?
You can change it in the options if you need to

F7 is the normal one for the autoload

If you want to load the map after restarting the game, go through the "community maps" menu and start the map normally first, then reload your game.

If you reload from outside the workshop, the rating screen at the end won't work.