We spent 2 weeks at Divi starting in late February and they did take out our trash when they did the midweek visit to clean. They did not come into the unit any other day during the week for garbage pick up, but they did provide some extra bags, so we took ours out another day when it got full.

Aziana is not at Divi but by Bobby's Marina, not too far from the Greenhouse in Philipsburg.
https://www.aziana.sx

Big Wood looks like it's about in the middle on the Philipsburg boardwalk. https://stmaartenboardwalk.com/listing/bigwood/