You say I have a cut-off, but what is the cut-off for YOU? It sounds like 240 years (like the USA) is too far, but somehow 180 years is that different?
And it's troubling that you think just because there's not a large group of people that you think their interests can be disregarded. I don't think the fact that there's only 3,000 Falkland Islanders makes their desires illegitimate.
I have no cutoff for the US. If the US occupies any island that another country has a more legitimate claim to, then the US should relinquish that island. The fact that it may be 300 years, 200 years, 100 years, or 10 years is irrelevant to me.
However, you have come up with some sort of arbitrary cutoff that you randomly came up with that magically lines up with UK activity. How convenient!
The only issue that I have some agreement with you is if the separation is too entangled, too established and thus too difficult to resolve. However, that is obviously not going to be the case for almost any island and especially an island that is thousands of miles away from its 'parent' country, whether it's the US or the UK.
The interests of the 3000 Malvinas residents isn't disregarded. There can be a transitional phase (say after 50-100 years so all 3000 Malvinas residents can be under UK control) and nobody is asking for them to be expelled. Morover, they could even be granted dual citizenship and Argentina is a very vibrant democracy.
Anyways, you are the one with the arbitrary cutoff date that magically blesses everything the UK has done. I don't even give the US a magical cutoff date.