IMO there are two firm and absolute requirements for a repository for your and the ASSRA's records.
The first is continuity. Whichever institution has responsibility for the records must have a program for storing and retrieving them, with an established and publicly-available procedure for obtaining information. Unfortunately I agree with Steve, Trinidad is simply not the place IMO. The school is basically a simple local-area-serving junior college with no research and/or curatorial program so far as I know. What's needed is a reasonably-well-known institution with an established reputation if possible, but in any case one that's likely to both preserve and add to the collection in the future as well as making it available in an ongoing & dependable manner.
The second requirement IMO is a method for the institution to make money on each information request. Not necessarily an actual profit, but at least enough $ to offset the expenses of the service. Most all museums includiing Cody charge a fee for any research and copying services, but the members of the ASSRA seem reluctant to donate their records to anyone who would charge a meaningful fee. I'll bet it'll be very difficult to find an institution or individual who would or could guarantee inexpensive access without some additional method of funding. Yes, the records & books are valuable & interesting in and of themselves, but not so valuable or interesting that a museum would grant free services just in exchange for them, as some ASSRA members seem to expect.
As Yul Brynner (The King and I) used to say, "It is a puzzlement!"
Regards, Joe