Specifically with regards to checks you've written that are cashed months later, do you keep it in YNAB with the date it was written.. or move it to the day it was cashed?
Agreed with jofo. Imo the purpose of YNAB isn't to track how much money you have in your bank account -- it's to track how much money you have available to spend. We already set aside money to pay for expenses we know we're going to incur in the future, and we don't let ourselves use that money for anything else. Philosophically, I feel like it's the same thing? You never know when the recipient is going to cash it, so you may as well consider it spent right away.
Alternately, I think it might work to put the transaction in immediately as "uncleared," but then mark it as cleared once they cash it. That way, it shows up as a transaction immediately, but you don't lose track of it not being cashed yet