For starters you could narrow down your point of departure
For example are you leaving Anchorage, Honolulu or Miami?
Non-connecting flights are as you have already figured out, are ones that depart from the airlines' hubs or gateways like MIA, or JFK.
The alternative if you are going for 1 or 2 weeks is to look in the paper or ask a travel agent for a air-only charter flight from your starting point, to PP and not a package with a hotel unless you want that as well. Charters tend to fly non-stop and not use hubs. Of course they have irregualr schedules and may add stops in the DR that they only tell you about when you get to the airport and they have seats that monkeys could barely fit in but apart from leaving via a non-stop gateway that is your alternative.
Swimming from Key West is also a possibility if you are a good swimmer and are not in a hurry.
