I don't think it is clear that one of your options is clearly superior to the other, so I suspect you pay your money and take your choice. It is very hard to make a choice if you are not on the boat because the description you give (or any possible description) does not give any sense of what the attitude of the crew is at this point. Crew being exhausted is a big issue. Have they considered heaving to or lying ahull for 6 to 8 hours so that they can get some sleep. Don't know the sea state but you say it is worse further soon.
Perhaps it is my attitude, but with everything else being equal - which it rarely is, I would be inclined to head to Bermuda after getting some sleep. I am trying to get to the Caribbean and Bermuda at least is in the right direction. If they go to Beaufort they are going in the wrong direction and still have to make up all that easting (I am assuming that they will continue their trip). There is a good sailmaker in Bermuda and any other parts they need can be shipped quickly if not available on the island.
Good luck to them.
Heading back to Lake Ontario for this summer. Relatively few stops along the way from Grenada. Martinique, Guadeloupe, St. Martin (must have something to do with the French food), then Bermuda, New England and up the Hudson/Erie Canal. We were going to go via Newfoundland and Labrador but June remembered that one of the kids is getting married this summer - details, details!