You might want to consider the islands without electricity
first. It seems logical that the cost to purchase land on an unpowered island should be considerably less than on a powered island and the cost for a powerful off grid solar/battery system is likely far less than you think. The biggest off grid improvements have come recently in the energy storage. Unlike the old lead acid batteries, the new generation of storage is nontoxic, nearly maintenance free, and long lived. Example;
https://www.youtube.com/watch?v=1EhnmWo2CZ8
It is feasible to power a good sized camp
with air source heat pump HVAC ("mini-splits") without problem all summer long. If you are going to be using the camp in winter however, you would need to add an auto start generator to the design. There are now "smart" solar inverters that are not only capable of controlling the solar array, they are also able to control running of the generator. Example;
https://solar.schneider-electric.com...olar-inverter/
You no longer need to look at powerlines or pay a monthly bill to enjoy a strong steady source of electrical power