At this time, you must apply to go to Anguilla, the rules are on this site:
https://escape.ivisitanguilla.com/

But, by November, that could all change.
Also note, self tests for departure from Anguilla are not allowed.

You have received some good suggestions, rates usually change from low season to high at most places on Nov 30, some additional suggestions:
Shoal Bay Villas on Shoal Bay East.
Rendezvous Bay Hotel on Rendezvous Bay.
Carimar Beach Club on Meads Bay