If only they could print more land.
But the thing causing the problem is Islam. We solve the problem by changing Islam.
Heck, it turns out Mahomet may have borrowed all that Korany stuff. At least they have found a document which suggests it is possible. "These tests provide a range of dates, showing that, with a probability of more than 95%, the parchment was from between 568 and 645." - lest we forget, the Prophet M was said to have started his inspired utterances in 610. So on a parchment-dating-only basis, there's a 41/77 chance the text was written beforehand by someone else. Something that somehow seems more likely than divine inspiration.
That's to say, it's another book that is just a book. Since the ground is shifting, it's a good time to consign some things to the past. It's a good time to permit the secular state and apostasy and interfaith marriage and women's rights and equality between believers and non-believers in an Islamic setting. As opposed to setting aside secular liberal virtues in favour of antique religious dogmas out of some strange notion of respect.
The island idea is a bit like trying to suggest a way to limit the problem of money in American politics without changing the Constitution. If you don't identify the issue, you won't solve it. Where major constitutional issues have evaded resolution previously (eg slavery), the outcome wasn't good.
The Roman Empire came to an end amidst an immigration problem. Maybe this is how it felt to see your culture diluted by waves of people crossing the Rhine. The funny thing is, those people were also being pushed.