"How does the pattern change if it's 'EVen I could pass THAT class!'? (Bolding 'I' since it already takes the capital.) Does the self-deprecation (presupposing oneself to be generally inadequate, even if jokingly) mitigate the attack?"
I've been thinking about this ever since it was posted -- it's an excellent question and not easily answered.
For my dialect.....
"'EVen I could pass THAT class!" still presupposes that the class itself is mickey-mouse -- one of those classes where just showing up and breathing quietly will get you a B.
For the "I" portion -- and using "Pat" as the individual's name -- I think there are two possible scenarios.
1. Pat has very little self-confidence, considers himself/herself stupid and a rotten student, and doesn't hesitate to say so, so that "EVen I could pass THAT class!" has roughly the meaning "Even I, stupid as I am, barely able to find the bathroom alone, could pass THAT mickey-mouse class!"
2. Pat doesn't consider herself/himself stupid, but for any number of reasons that would be available in context has a standard practice of putting herself/himself down in front of other people, so that "EVen I" -- and I'm far too courteous a person to say aloud that I'm a pretty decent student, so I'm pretending that I think I'm not -- could pass THAT mickey-mouse class!"
I know no way to distinguish the two alternatives using only written language; you'd need all the intonation and tone of voice and facial expression and the rest of the bodyparl.
It interests me that what's done to the "EVen X..." part of the utterance has no effect on the "...THAT class" part. Very stable, the negative presupposition that goes with "EVen X...". Which, you perceive, is there even when it's not there, like the traditional "Understood 'You'." That is, "JOHN could pass THAT class!" and "A CHILD could pass THAT class!" and "I could pass THAT class!" all have an "Understood 'Even' at the beginning.
[You maybe need a smidgen more stress on the content of [X] when the "EVen..." isn't lexicalized; I'm not certain, but I think you do. If so, that's neat, phonologically, and would be a pretty little rule.]