What percentage of the booking are you out if he doesn't pay?
If you take the payment, then VRBO needs to trust your records. If they take the payment they need to explain to you where the money is.
I completely appreciate not wanting to lose your status, and there is definitely a trade-off. What you've explained so far doesn't sound worth it though; I think you need to hold firm and possibly cancel if he won't go along with your policies.
Talk with VRBO though, and ask to escalate the call if needed; it sounds like they have gotten involved and made it harder for you to properly and legally run your business...so they have now made themselves partially responsible for this booking. This will likely be a very frustrating call until you reach the right person (sometimes I've had to call back and try again), but if losing the money, status and upsetting the HOA is the priority then stay on it until it gets resolved.
Two notes from the last time I called VRBO:
1.) I use a PMS, so there is actually a different department for that, and they were very helpful (because the payment and booking process is different). If that's your situation, mention it to the operator, so you get the right department.
2.) The reason I was calling was to help a guest cancel after they checked in. They had misunderstood what floor the unit was on. We agreed they'd be happier somewhere else and they were offered a full refund. The time I spent on the phone with VRBO trying to fix it (and the risk of losing a few nights of revenue) was worth ensuring no one had a bad experience/left a bad review.