https://en.wikipedia.org/wiki/Estoppel#Reliance-based_estoppels
HOA going back on their words, this is called estoppel. You relied on their words and suffered damages (such as cancelled booking). You should hire a lawyer to write up a letter, saying you can stop after current bookings are satisfied. Otherwise, they can pay you damages for cancelled bookings, and you will sue if they don't pay up.
No need to file the lawsuit, I think a strong worded lawyer's letter is enough.
Your case is optimistic because you have evidence of their promise broken. Usually people only call and receive a verbal assurance, that's not evidence.
Keep in mind sometimes HOA regulation might say they cannot be estopped by the management company's staff. This means no matter what they tell you, it's your job to study the HOA regulation and find out the answer (such as no short term rental). In that case you'll just have to bite the bullet.