Memes

Interesting info and I'm not arguing against your point, but that source doesn't address their point at all. The cited source covers recent demographics. The previous user is referring to events that occurred in 1947ish. The time periods are not close enough to be relevant to each other, especially considering the massive changes that occurred throughout that period in the area.

That's kind of like if someone said that the Caribbean was entirely populated by natives when the Europeans showed up in 1492, and someone responded with demographics from the 1570s after the Spanish had established settlements in Cuba, Puerto Rico, Jamaica, Trinidad, and conquered the Aztecs to dismiss the initial point. The demographics are going to be vastly different. It kind of sheds doubt onto your rebuttal since there seems to be a logical disconnect.

Does anyone have any sources on the demographics right before the British invited Jewish people to move to the Levant?

Ashkenazim have European surnames because Europeans literally forced them unto Jews. Austro-Hungary, Russian Empire - both had policies for giving Jews "local" surnames (for taxation purposes). It's how you get Jews with German surnames in eastern and central Europe (i.e.the ones you have listed), and how you get Jews with Ukrainian and Russian-ish surnames in the appropriate areas (see Abramovich, Litvak)