5a. There was an united empire of 16 provices full of Yoku. Yet we haven't heard of them before the cataclysm.
5b. There was no united empire of 16 provinces with distinct cultures. Yet they didn't come to Tamriel in the cataclysm.
6. Because 5a and 5b are very unlikely, 2 is also very unlikely
7. Because of 6, the Empire of the Left Handers likely did extend beyond Yokuda. The only culture that has ever been so widely extended is that of the Aldmer.
And this is where your logic breaks down. First off, a "province" can very well vary in size. 16 Yokudan provinces (which are dividend by cultural boundaries) may only size up to 9 Tamrielic ones. After this, see my response to 5b below.
Also, their common naming, "left-handed" elves is odd in an of itself. They were unlikly Aldmer. Why? First off, why would they be designated as "left-handed"elves as opposed to plai old "elves"? Also, if Left-handed does indeed imply an adherence to left-handed philosophical principals, then clearly the very conservative, very tradition-based, and very utilitarian Aldmer don't seem to fit the bill. Saying they are just baseline Aldmer seems a cop-out.
Why should not everybody, be exclusively Redgaurd? Obviously the cataclysm wasn't fast enough to kill everybody at once or even they wouldn't have made it out, but if there was enough time to the Redgaurd to get out, why not for other people?
Lets say Tamriel was the one set to sink. Do you think, for instance, the poverty-ridden, sheltered and racially discriminated Argonians would stand much of a chance at survival? Probably not, as in the same way many of the less well-off peoples of Yokuda porbebly died when their home did.
Could the others have escaped west, to Akavir? The 3rd PGE mentions that there are perhaps some undiscovered races over there, or it could account for one of the ones we already know about.
I think this might hold some credence. The Japanese cultural artifacts in Redguard culture imply some Akaviri presence on Yokuda, and I think it is possible one of the cultural groups living on the continent was Akaviri in origin.
So we're 100% certain that this is some other type of 'Left-Handed Elf' and that it's only coincidence that they share the same nickname as the Dwemer? This is a serious question, I'm not trying to be a smart-ass.
Left-handed implies a certain level of similarity in mindset to the Dwemer, but I don't think its very likely they were
actually Dwemer, just similar in intention.