I'll say it again, contact the property manger/listing agents/owners for the properties on the islands you are considering and ask about long-term rental rates. Almost all of them will give you reduced rentals.

On the island where I live visitors rent condos and villas by the month, "for the season" (usually 3 to 4 months), for 6 months and for the year all the time. They ALWAYS pay something much less than the standard weekly rate. I have quite a few friends and acquaintances who do this every year on numerous islands.

I also have several friends that rent out their homes and I know they would definitely offer someone reduced rates if they rented long-term.

It is common practice but you'll rarely see long-term rates advertised on websites since those are geared town short-stay tourism. Hint, the longer the rental term, the better the rental rate will be.