In the face of some readers' scepticism, I'll have more to say about merely-emphatic even in a future post. Meanwhile, I'd like to suggest that current even trends may have been influenced to some extent by a 1960s pop-culture avatar of even as a wide-scope emphatic particle, namely Snagglepuss:
Heavens to Murgatroyd! Somebody has terribly large knuckles! To knock with, even!
From the same cartoon, around 2:49:
Heavens to agony! Somebody hurt! In dire pain, even!
And around 4:14:
All out! Last stop, even!
Whoops! I'm all apologies! On account of I must be a little rusty. Stale, even.
Major Minor: Don't call me, I'll call you.
Snagglepuss: I wonder if he knows my telephone number, even.
These examples exhibit Snagglepuss's trademark phrase-final placement of even, as an adverb taking scope over the whole preceding phrase. But you can (and maybe even should) interpret these examples to express not mere emphasis, but also the standard 20th-century scalar sense of even as "Intimating that the sentence expresses an extreme case of a more general proposition".
However, with constant use, Snagglepuss's phrase-final even gets bleached to the point where there's not a lot of scalar implicature left — if any. Consider this example, from the start of another cartoon, where Snagglepuss bemoans his captive status and then sees a chance to escape:
Oh! Would that I were free! Unfettered and uncaged!
To think that I, king of the jungle, should be so lowly treated!
Besides, the food is abdominable.
But hark! Or is it herk? The cage door is open! Ajar, even!
In most of the examples that we've seen so far, Snagglepuss's final even follows a re-statement, even if the parallel phrase is not clearly "an extreme case of a more general proposition." But it's sometimes used without any similar parallelism, as in the telephone-number example.
Or consider this case, from Fraidy Cat Lion, when Snagglepuss unexpectedly encounters a giant mouse, and says, without any previous parallel construction:
Huh? Heavens to Murgatroyd! A veritabububble frankenmouse monster even!
Or this, from the start of Arrow Error, where Snagglepuss is fantasizing about Robin Hood:
Hand over the gold, and the charge-a-plates, or thou shalt feeleth my sturdy bow and arrow even.
You can certainly make up some scales on which a encountering a giant mouse or using a bow and arrow is an "extreme case of a more general proposition". But after a while, it seems to me, Snagglepuss's phrase-final evens become just another signifier of his emphatic campy flamboyance.
And maybe the generation that grew up watching Hanna-Barbera cartoons felt the same way, and transferred this mainly-emphatic sense of even to uses like "What does that even mean?" or "I don't know what that even is". (Thereby moving back towards the sense of <i>even</i> current in Shakespeare's time…)
[If you want to know why the YouTube videos start muted, it's not my fault. Sorry anyhow...]