>They'd sell their stake in it and go for real resources locally. The actual real resources they consume are going to be made up for by the upper-middle class having less.

That is not necessarily true if you can produce more of the resource. The extra money would drive up prices and thus make it more profitable to run a company that offers the resource. Housing is artificially restricted but the technology to build denser housing exists. Taking the island is not really a sound strategy though, because it is much more efficient to just borrow money and give it to people through government stimulus. CPI inflation will eat at the value of unproductive capital like the island away on its own.

>If anything is done about income inequality, it is probably going to involve bringing the above-median types more into line with the below-median earners.

There is no meaningful difference between lowering the top and raising the bottom. Wealth tends to flee easily so increasing the bottom is a more reliable strategy. CPI inflation is generally a force that does both at the same time.