While I loathe two of the words in your heading in relation to travelling (those being "Ultimate" and "Experience") I understand where you are coming from....In three weeks you don't have enough time to do Puerto Rico, in me estimation....I would fly to Cancun(stick with me) and immediately leave for Merida, then look at several of the ruins around there and several of the small towns. Head back through Cancun (without going to the "horseshoe of death" and go visit Playa for a day of lying around, and then go down to Tulum for my sentimental favourite Mayan ruin ( the Mayans liked beach resorts too, it seems). Pass through Belize. Stop in the Cayo and ask around for the ruins behind the waterfall if you want....Really fascinating and lying in situ Then go to Florese Guatemala and enjoy yourself there...Taking in Tikal and enjoying the nightlife. Hot foot it back to Cancun along the route that got you there, stopping in Caye Caulker if you have the chance, and then go home...
The alternate route, to me, would be to go in a straight line from Guat City(avoiding the city) Antigua, ChiChicastenango, Quetzaltenango, Florese and Tikal, San Ignacio(The Cayo), Caye Caulker, Chetumal/Corozal, Tulum, pass Cancun and go to MErida....back track to Cancun and out.
This is all with about three minutes of thinking...I am sure there are better ideas out there.
D