Film is a tricky subject, more so these days, as you've noted. Fuji, with its opaque containers, has usually been my film of choice. I haven't traveled with any lately, but my recommendation has been to take the containers w/ the film out of the box and put all the containers of film in a ZipLock bag. Carry this with you, then request a hand-check of your ZipLock at the x-ray machine. I know you don't want to make a scene, but insist to speak to a supervisor if the attendant will not let you hand check.
Despite what these poorly educated people will tell you, x-ray damages film, as it is cumulative. They have been told to tell you that only high speed film gets affected. Wrong. ASA 100 film that goes thru the x-ray in Salt Lake City and Houston is now affected as much as ASA 200 film. When you go from Belize International to San Pedro, it gets another dose, and assuming all machines are giving it the same time/strength of exposure, your ASA 100 film has now been exposed to enough radiation to make it fog like ASA 400 film would.
Exposed film is just as fragile, so a zap when leaving Belize makes it ASA 800 film. Going thru Houston on your way to your final destination (I just picked Salt Lake City as a starting point, but you get the idea), that one last blast now makes it ASA 1600, what most of us would consider ultra-high speed film. If just ONE of those operators stops your camera bag for a better look and it spends just twice the normal time under X-ray, you can double that. I don't want the possibility of that kind of fogging on my film. Remember, when dealing with an operator or a supervisor, their job is to run a machine, not be knowledgeable about the effect on film. An argument will probably get you nowhere, but if you can avoid just a couple of these machines, you're ahead of the game.
Leaded film bags are available and you may want to get one for your film. Once it goes through the machine, someone may ask you to open the bag. That is your best deal, because you are now guaranteed a hand-check. Since you've discarded the box the film came in, you make it easy for the security people to do their job.
In Belize, you'll generally find slide film old, poorly stored, expensive and seldom in 36 exposure rolls. I always shoot 36s because I believe fish know when you're out of film. I've seen people who use Kodak film that comes in black containers go to a local film processor and get some opaque Fuji cannisters for travel.