Is there a way to coordinate between those with space and those looking?
There is no formal place or process for that. The best options are posting here and on FB. If you have local members you're in contact with that is usually where I start. A separate thread dedicated to that (e.g. "STAR 21 looking for a room / roommate") may work best but posting it here is also probably OK. The good part about a dedicated thread is it all goes there, and there may be less double posting of the same thing in multiple somewhat related threads.
Also my experience over about 20 years in this club is that most people have their normal travel group and roommates. Not many are looking for some person to share a room with. One time when my roommate cancelled for Mail Pouch I posted in some places, and another Ohio member who had a room with 2 beds to themselves offered to share with me. There was no room shortage and they were perfectly happy with a room to themselves. That isn't meant to discourage people from looking for roommates only an attempt to set your expectations and finding a partner. Same can go for looking for a group to ride with, some may welcome an unknown rider, others may not.