Yeah, that is another thing that helps, is if every letter made requires an active response from the other player(s). In my epistolary game and this other recent epistolary game, every letter has a body where you advance the story, but it also ends with a specific question for the other player to answer. So the other player has a clear prompt to write from, and the other player is waiting for their answer. The series of answering then asking questions keeps the story moving forward.
That works partly because they’re 2 player epistolary games. The answer-and-question format would require some tinkering to make it work with 3 or more players.