entropy, it was actual purchased by Mortecai Noah ... looking for an online reference, I discovered I was off in my time reference (I said 'late' 19th century; it was actually 1825 as you said.) The only Eli Avivi of whom I amaware founded the quasi-independent state of Akhzivland in 1952, within Israel itself.
Not sure on the size, but the CoC in Grand Island says it's the largest freshwater island in the world ... if it is in fact 27 square miles that makes it larger than Manhattan. New Yorkers did pretty well with Manhattan; and given the surroundings a sovereign Jewish state on Grand Island would not have had to worry with squeezing themselves to death trying to fit the entirety of their population into an area so much smaller than Isreal (just under 450 sq mi) and would not have the nagging problem of an insanely hostile indigenous population, neighbours, etc.
Grand Island's official website is
here.
An interesting history of the island, which mentions the plans for a sovereign Jewish state in passing, is
here.
Phaedrus