Not a good idea
I have never tried it, but some of my sailing friends doing Canal transit eastbound will sail the following route to the Caribbean: Enjoy the San Blas Islands, sail to Cartagena (to get a better angle on Florida) , then try to lay the passage between Cancun and Cuba in one tack. From there you have choices on how to best approach the Caribbean.
This is second hand info, but comes directly from boats that succeeded. I am told you can go east from the Canal only a handful of days in the year. I am told that very large motor yachts have been stopped in their tracks and had to retreat. It is reputed to be the most impossible passage on earth. Just saying.
Good luck and godspeed with your plans,