We have done the trip you plan twice. Belizesailor has it right that April/May is preferable but early May/June is not unreasonable.
Important points are:
The charts/navionics are out by at least 400 yards until you reach American waters. We stay at least a mile off the reef.
Straights are very bad when the wind
is from the north
The Gulf Stream
can be ridden all the way and in Belize/Mexico/Florida is close in.
El Cid marina in Puerto Morelos Mexico
south of Cancun
is a good refueling stop but "local taxes" when you check in are exorbitant, over $300 to check in and out. Isla Mujeres may now be a better stop.
Puerto Morelos, Yucatan: Expensive for Clearance — Noonsite
Dry Tortugas/Fort Jefferson make a nice stop and the charts
are fairly accurate. No services what-so-ever.
is a free anchorage but a $30 taxi ride to check in.
Coconut Grove Sailing Club is an excellent place to stop and replenish for the journey north. Coconut Grove Sailing Club