I haven't stayed at any of the three resorts you listed. But my wife and I did stay at Turneffe Island Resort twice for a total of three weeks and it's very close to Blackbird so maybe this will help.
Like Blackbird, TIR is right on the beach. The wind was near constant and strong. No issues at all with mosquitos. But on the few occasions that the wind died down, the sand fleas were ferocious. Compared to a mosquito bite, which I often don't even feel until later. sand flea bites are painful and you'll instantly know it's happened. They often draw a little bit of blood.
So when the wind died down, we stayed inside. But it really didn't happen often, maybe three times in three weeks. We were there both times in mid-summer.