Sorry to butt in late, and no I have not really read your arguments, but honestly it is closer to what you stated: “leaves it up to Congress”. However “crime” is relative, and again, you only see it as part of the phrase “high crimes”.
I prefer to go to the Founders for what they meant; evidently Congress (Reps) thought being biased was enough of a “crime”.
https://en.wikipedia.org/wiki/Samuel_Chase
Chase WAS impeached (i.e., he was charged), he just wasn’t convicted (presumably, they failed to prove he was “biased”, not so much that it was a “crime”).
Honestly, Congress can impeach for whatever it damn well pleases.
What Congress passes as a crime may "relative" or random, but "crime" is what the Constitution or what federal statute says is a crime. Otherwise, you're truly living in anarchy as well as tyranny. Anybody can accuse you of anything - Jacobean Reign of Terror revisited.
It’s “high crimes” and “misdemeanors” (Art. II, Sec. 4) which currently means “low crimes”. I’ll have to research to see what “misdemeanors” meant at ratification.