I have wanted to do it for five or six years but haven't gone to the trouble to put together the chase boats, etc. The Straits can be an intense place for waves and current. In setting something up like this it would be good to try to pick the best conditions feasible for such a thing, it isn't a record attempt, just something to do for fun. This as opposed to the Key West to Cuba record crossing which was done in some of the most undesireable, challenging conditions short of a hurricane, conceivable for that route.
In a crossing you would need to allow for the set of the Florida Current, perhaps about 3 kts. when calculating your course. There are Internet resources that provide info on the alignment of the Current and perhaps velocity estimates as well. Compensating for the set of the current would add some miles to your trip but should allow you a landfall say in the Bimini's.
The wind is a tricky proposition. Reliably strong winds in the cooler months are out of the NW and NE. NW is a deal breaker for a more reasonable crossing. Strong winds opposing the fast moving waters of the Current setup nasty, steep and big waves rapidly. If you rode up from the south on a beam reach you would be riding into big, nasty ragged breaking waves across the straits. I piloted a boat back to Florida at 16 in strong NW'ly winds requiring me to surf the boat using the throttles most of the way across in 8 to 12 ft. following choppy breaking seas to avoid broaching or pitchpoling. In a honking strong cold front blasting out NW winds you can see how the horizon goes ragged and foamy over the Florida Current in the distance.
NE can really kick things up too, just not quite as badly as NW. In using a NE wind you would have to ride against the Current, not a first choice.
SE to E are fairly reliable directions in the warmer months. E would be a bad proposition requiring a major offset to the south and riding close hauled. SE would be the direction I would try for. Of course S is even better but not a reliable, long term direction.
Winds away from Florida and the Bahamian plateau can change outside of land effects. This would have to be taken into consideration as well.
If you could pick a day with good SE winds, say around 15 to 20 mph for the width of the Straits, I would say a start off of Ocean Reef or Tavenier in Key Largo might be the ticket. I would have to do the course plotting to see where an ideal starting point might be. Ideally you would have a fairly small number of riders and two to preferrably three boats. One boat would follow the course for the kiteboarders to use for reference with the other one to two as support boats. In the Key West to Cuba crossing the waves and wind were nasty making the boats fairly bad places to be. The speed overground of the kiteboarders was low as well at around 11 kts. I think. Riding in lighter winds out of a direction less prone to kickup an ugly, adverse sea for a fun crossing would make sense.
There would be more to it than this but these are some starting ideas.