Yes, check on your options for filing in your home state. That might or might not be possible.
In the meantime, if you want to date, date. It's not like you're IN a marriage anymore, and your ex is moving in with someone. It's not cheating if you're waiting for the waiting period to expire--ESPECIALLY when he's moved on.
OTOH, don't feel the need to rush into a new relationship. That kind of behavior led to a lot of bad outcomes for me.