With all due respect to your particular situation, and as a timeshare owner myself, albeit not at Pelican, I hesitate to suggest this but I'm afraid your "initial investment" is probably already long gone.
If you've actually owned and used your timeshare since 1984 and as you have stated, you have enjoyed it and travelled all over the world with it, that is perhaps what you should view as the payback on your 'investment' and consider its a done deal.
My information is really generic with regard to timeshares outside the US but I'm inclined to believe you cannot sell it and transfer title to another owner without having clear title in the first place and with outstanding AMF or assessment you don't have clear title.
I know it's a hard pill to swallow but if you really have no inclination to use it again and want out, walking might just be the only answer to your situation. But know in doing that, you now have no rights of ownership and they probably could, though rumor has it they don't, come after you.
Again, I'm not a Pelican owner, but I'm thinking this is the downside of timeshare ownership in areas where there are no protective laws in your favor. As a timeshare owner elsewhere on the island, I see people walking away all the time because they just want out so I'm doubtful if you'll get big dollars for your Pelican units even if you pay all the fees and then try to sell them. Take a look at E-bay resales and Holiday Resales for an idea of what the resale market is like.
Sorry to be such a downer, but this is the experience I've witnessed and heard of from personal friends who have found themselves in your similar situation. Good luck and perhaps others who actually have units at the Pelican can be more positive for you.