A number of expeditions to the south of Belize were undertaken by the SWCC.
A very useful website was compiled, but now offline. You can browse a capture of the website on the WayBackMachine.
https://web.archive.org/web/20161003025804/http://swccbelizecaving.co.uk/
Worth 49 seconds of your time :-
http://www.youtube.com/watch?v=aKFNunW_O0k
We visited part of the Chiquibul Cave in 2016. https://en.wikipedia.org/wiki/Chiquibul_Cave_System A grand adventure it was being in a remote part of the NP and near the Guatemala border. There was considerable bureaucracy involved and we were accompanied by a group of armed rangers to protect us. I expect any trip to this part of Belize would be difficult to arrange. Take Nick Williams up on his offer for more info.
I'd go to Phil's website, has the latest info on useful contacts. Ive been out nearly every year since 2002 training the guides, and getting info about the caves, we operated in Southern Belize, Toledo District, if you want the link to the report send me your email. I have many friends out there and PG has changed an awful lot.