A prepaid debit card sounds like a good idea for travel out of the country but I would still carry a few hundred dollars cash for taxi, tips, souvenirs, etc. Last year we were in Cabo and we didn't exchange any money for pesos, everyone seemed to be happy with US dollars.
$3K is a lot more than I would spend but I guess it depends on how much you plan to do, excursions/tours, etc.
I don't know how a big a tipper you are but I carry a lot of small denomination bills (ones and fives) for tips.
If you pay for everything up front(including airport shuttle) at an all inclusive place you can not spend another penny if you don't want to.
A couple of other things:
You can probably purchase tours through the hotel or from people on the street. The hotel will be less risk but I have purchased tours in town and didn't have any problems.
Hotel may advertise free Wifi but it may not be any good, only works in the lobby, purchasing the good Wifi is probably worth it, maybe $30 for three or four devices.
Have a good trip.