To counter your counterpoints....
Hemme, Master Rhetorician
The counter to this point is in his title. Rhetoric is the art of effective or persuasive speaking. It is literally the art of impressing and persuading others through speech and the written word. Master Hemme takes Herma's illness as an opportunity to make a power play. Its an election, and elections mean politics. We have been shown through his characterization that he enjoys having power over others, perhaps too much. He is vain, materialistic, and he is convincing. Despite how Kvothe depicts him to us, he is a clever and conniving man. Herma's sudden illness was the opportunity he needed...and its sudden onset is suspicious in and of itself, considering Hemme's implied allegiance with Ambrose, and what we know Ambrose is capable of doing/have done to make his life easier (Plumbob, dissapearances, assassins, etc.).
[Hemme] was either too cocky or too terrible at Sympathy to defend himself
This is a weak argument. You forget that Kvothe is also cocky, and Hemme immediately recognized that trait (because like knows like). He has no reason to believe that a 15 year old raveling little prick has any ability to harm him whatsoever. And for someone who's used to having a gram protect him from sympathetic attacks, what reason would he have to make any move to defend himself? I don't recoil and take cover when a chihuahua barks at me, because I don't believe it has the power to hurt me. Then it bites my ankle and I am both surprised and pissed. But let's take this even further...Ambrose and Hemme are friendly, this is strongly implied. By the time Kvothe does his little mommet trick, he has already embarassed Ambrose and acted like a cocky little shit in front of Hemme. Its not unreasonable that Kvothe did exactly what Hemme wanted him to do, so that he'd have grounds to have the ravel expelled, and be rid of this impoverished child that is making a mockery of everything Hemme believes the University stands for. (Making lots of money and powerful political allies, in case that wasn't clear).
pretty sure the Masters of the University elect a Chancellor based on whoever has time to accept the responsibility...
There's no evidence or anything to give us any indication as to why certain Masters get elected over others. All we know is the Herma was the Chancellor for some time, Hemme got elected recently, and that Elodin was chancelor for a time. Can you even remotely imagine a situation where Elodin would volunteer to the other Masters that he has the time and desire to be Chancellor? I can't. We don't know why he was elected, we don't know why anyone was elected, and we can't be "pretty sure" of any of the reasoning behind their elections. Elodin being Chancellor is the wild card that makes the election process a mystery to us. I never claimed to be sure of why Herma was Chancellor, I just suggested that him being one of the few people in the World to know fluent Yllish was an interesting coincidence in that he was also the most powerful man in the University. A place Elodin has blatantly told us was established primarily for Namers to explore their art. A lot of the old traditions from back when it was a Namer's club for Namer's have stuck around. And that make's Herma's appointment as Chancellor very interesting to me.
It's also heavily implied that not all of the masters even know any Names at all.
How is this implied? I'm genuinely curious, because from my readings I've had the exact opposite implication. Perhaps this is just a matter of perspective?