ok i have a new idea. you should look at palm island resort in the grenadines. using their web site you can fly in 8 hrs with one stop both ways. it is a deluxe resort, it is ai & it is in easy day boat trip to some of the best snorkeling in the islands - tobago cays (not the island of tobago). you would have plenty of privacy.
you'd fly to barbados so if you wanted to spend a couple days on a larger, busier island you could do so easily.
http://www.palmislandresortgrenadines.com/

Such a thing exists, but most of these villas are quite luxe (i.e., more than $20,000 per week, albeit for a villa that will sleep 6 or more people). You can, for example, rent a villa at Round Hill in Jamaica and have breakfast in your villa and other meals in the resort's restaurant (they do sell all-inclusive meal plans). It's a resort, but a very small and exclusive one. That might be your best bet. But again, this will be expensive.

There are probably other ways of doing an "all-inclusive" deal at a villa in the DR for a much lower price. There are, for example, villas offered by North Coast Management in the Cabrera area of the DR. These can be fully staffed, and you can pay for all your meals and drinks as part of a package. Only the largest villas are going to come with a full staff, but the prices in the DR can be as low as $1,000 per night for a villa for 8 people, and you can pay extra for food and drinks as part of the deal. There are similar villas in Jamaica. Just be aware that these aren't always on a beach.

But most any good villa manager worth his or her salt can arrange for a private chef to come in to deal with meals and a maid for daily service. You can do this in a smaller villa in almost any island in the Caribbean if you are willing to pay the price.

If you are willing to pay about $3,000 to $4,000 per person for the week, you can arrange almost anything. If you are willing to pay $2,500 per person for the week, you can probably do this on a smaller island with a less sumptuous villa. But this would all be based on a group of 6 or 8 people. With fewer people, the cost per person is going to go up dramatically. But this is certainly cheaper than a resort like Sandy Lane in Barbados.

I just reponded to your Couples and Swept Away thread. While doing research on Jamaica I looked at the Moon Dance Villas. They are located directly on the beach in Negril and are listed as all-inclusive. I think you gave a budget of $4,000 - $5,000 total for 5-6 days on another thread. There's a one-bedroom villa that they call the honeymoon villa. Since you are going off-season it might work for you. (I haven't stayed here.) They all look very nice and get good reviews on Trip Advisor.

http://www.moondanceresorts.com/villas/

What about Blue Waters in Antigua? Great All Inclusive option and the food is fantastic. They have many types of rooms and a private villa on property.

Really want to do Antigua but t he airfare kills it. The flights are long and most, if not all have a 15+ hour lay over, we're only going for 7 days, and that kills it.

Right now we're considering Couples Negril and Turtle Nest Inn Grand Cayman.

Here is an all inclusive vill in St.Maarten Dutch Caribbean: http://www.caribbean-villa.info/all-inclusive-caribbean-villa.html

If you don't want to do the "AI resort thing again", then I don't think you will want any of the Couples resorts. Which AI did you stay at before?

The Turtle Nest Inn in Grand Cayman is not AI. It's condo/apartments for rent. You might look at the Reef resort on Grand Cayman instead. It a small hotel, quite far from 7 Mile Beach, but it is AI for that reason. You'll probably want to rent a car.

Also, look at Sunset Palms in Negril, Jamaica. Small AI hotel. It's across a street from the beach.

Check out this website www.islandbreezevillas.com to view some oceanfront and beach front properties that have maid service 5 days a week included in the rental rate, chef services are available. These properties also have a private pool and are all private villas.