Because I have flown two different Skymasters from Miami to Boise and extensively over water routes, including a trip from St. Thomas (Virgin Islands) to Miami, I have given considerable thought to your type of question.
Quick/rough numbers for a non-turbo: cruise speed 140 kts (at a fairly economical power level), 20 gal/hr (running by the book, leaning to about 60-75 deg rich of peak), 125 - 145 gal of usable fuel (with extended-range tanks, depending on model year).
Your trip (Brownsville to Managua) is 1025 nm. With the above numbers you need 146 gal, even before you allow for margin (and on a trip like this, with inhospitable terrain and infrequent airports, I would counsel 1 hour) and for take-off/climb (figure ~ 5 more gal).
Solutions (with opinions in parenthesis): wait for a healthy tailwind; equip your aircraft and learn how to operate at lean of peek (voids most engine warranties, not recommended by engine manufacturer, but I think it's OK if done properly); add after-market extended tanks (after a recent crash and subsequent findings, not something I recommend); and my favorite solution by far, which is don't be silly and do stop en route (it's under 700 nm to Mundo Maya Int'l Airport in northern Guatemala).
Pushing the envelope on a trip like this is NOT a good idea. Even on the 700 nm trip, make sure your aircraft is perfect, you understand management of your fuel system (I have a page on this at my
www.SkymasterUS.com "backup" website), and you have accumulated actual data on consumption from prior trips.
Good luck.
Ernie Martin