First of all these websites, backed up by the GDSes as Stephen said, do not have a very good coverage of hotels (yet, it’s growing fast). There are still plenty of hotels to aggregate. And for hotels, getting aggregated usually means stricter conditions on their prices (little flexibility and high fee). And the main reason is that most hotels are not owned by large companies but individually owned.
So I would not expect, especially in a remote area, that you find all hotels on these sites. First you should extend your search to hostels (they have private rooms with private bathrooms), b&b, pensions, … sites like hostels.com or hostelworld.com allow to search for more than hostels. You can try airbnb, couchsurfing and the like.
I would try the tourism board as you did, but that works only if it is touristy. I would bet more on the directories. In most places of the world they are called yellow pages. And there you shall find a list. I can also think of contacting the ferry or airline company that brings you to the tiny island. On their website they might have a list of activities and accommodation. Give also a try to the guidebooks, they are usually done for that purpose. Maps like Google Maps or OpenStreetMap also display accommodation options, even though you should always double check they actually exist.
In the end, if hotels that have a website/can be booked online are still very expensive and you suspect some hotels are not online you can still show up there without a booking. If the area is not big you can cover it fast but if it is an island you should have a backup plan to be able to leave the area before the night not to be stuck there.
I remember getting to a Croatian island off-season and the hostel phone would not ring. I showed up and I could get a room for cheap, but I planned to take the ferry back if I could not find anything reasonable (and it was so dead I really was not sure it’d work). So yeah sometimes you can just give it a try.