What time of the year are you planning to travel? Are you traveling solo? If not, is your travel partner also a diver?
The diving in Jamaica is not the greatest and I have never heard Barbados described as a great dive destination but I don't know that for myself. I can't think of any options in the T&Cs that meet your requirements.
Cozumel and Roatan are probably the best choices from your list for your budget. Look at the 2 for 1 special at Anthony Key Resort but airfare can be difficult and expensive to Roatan.
https://anthonyskey.com/specials/two-for-one-special/
Finding a place with good shore diving on a house reef that is included at no extra charge can give you more diving opportunities without additional expense.
Cobalt Coast is an all-inclusive dive resort with a house reef and it may be the best choice for you on Grand Cayman but it is above your budget for 2 weeks, but you can often find reasonable and easy airfare to GC:
Grand Cayman Dive Packages at Cobalt Coast Resort
The Plaza Resort in Bonaire has some economical deals and includes shore diving but the airfare to Bonaire can be expensive and difficult.
https://www.plazaresortbonaire.com/en/all-inclusive
You might also consider a week on an all-inclusive Blackbeards liveaboard cruise in the Bahamas, paired with a week in Southern Florida:
Blackbeard's Cruises Official Website - Bahamas Dive Liveaboards
Why do you only want to look at all-inclusives? If you have the leeway to prepare some simple meals and also eat out for some meals, then you can often save money - and that can contribute to an inexpensive dive vacation, especially in a place with cheap shore diving available like Bonaire or Curacao.
When you are comparison shopping for a dive vacation, be aware of hidden expenses (taxes, fees, transfers, service charges, and exclusions) and make sure that you understand the full costs and are comparing "apples to apples" before making a decision. For example, there are 19% hotel taxes in Roatan, and sometimes the cheaper lodgings don't include air-conditioning - or AC is only available in the bedrooms, etc. The biting insects are bad on Roatan so you really do need AC.
There are 13% hotel taxes in Cayman and some venues also add on service charges, but the package price for the Cobalt Coast link that I posted above already includes: transfers, taxes, lodgings, meals, and hotel service charges, and the diving is included but not the dive shop tips.
Sometimes a dive destination seems like a bargain, but the airfare to get there can be expensive and difficult - so my advice is just to be aware of all the pros and cons before making a decision.
Good luck with your search!