I have a completely different approach to this … rather than bargaining with the professor.
The night before seeing the prof, I’d shower well and then put on a good shot of -none (maybe 10 or 20 mcg for me) with no social pheros at all. I’d spray the none where I can smell it while I sleep.
Then, the next morning, I’d call on the prof unannounced (assuming he has AM office hours) with my “dimmed down” -none signature, well blended as I slept.
And I would say something like this:
“Hello” (* wait to make eye contact )
*
“I’m wondering whether you’ve ever considered changing a grade at a student’s request.” (* of course he has ~considered~ it; if he says no, skip ahead to the goodbye sequence *)
“I don’t want to give you excuses, or plead some exceptional circumstance. I ~am~ curious to know what you’d expect of me to change my grade from X to Y.”
Then … just shut up and nod your head; force yourself to keep breathing and if he just shuts you out or refuses you, then do the goodbye sequence: say “Thanks” and then make some unrelated observation “It looks like the football team might win today, doesn’t it?” and turn and walk away. He’ll know how to contact you if he reconsiders.
Teachers like to teach, even if they don’t like preparing and attending and leading class sometimes. And teachers have a difficult time letting a mystery walk away.
So, afford the teacher the opportunity to seize a teachable moment, and also do not destroy the only currency you have … mystery … by blabbering some kind of tale of woe, which just invites disrespect.
The mindset for this interaction is man to man. Your phero usage here is not to create an “edge” of superiority, but to establish yourself as an existential equal. Any hint of “son coming to father” or “athlete coming to coach” or “student coming to teacher” puts this all wrong. Inquire, do not supplicate.
You’re a guy … an adult … with a question for another guy … an adult … you happen to interact with.