Ugh, what a douche.
Unfortunately, the best way to get what you want is to be sugarry sweet. You have to set aside the vindictiveness, anger, etc for long enough to just get him to do what you want.
Wait for him after class. Apologize for coming across as rude, mean, whatever, say you are sorry for taking up his time, but, etc etc (every simpering, lily livered thing you can think of essentially), but you need to discuss something very important with him.
Say you know it wasn't on purpose, you completely understand that these mistakes happen, but this is your entire future riding on the line and, you know it is inconvenient and you don't mean to be a bother, but this needs to be addressed. Offer to help however you can (if you can have whatever forms are necessary on hand, that'd be good) and be obsequious. Cry if you can because this is so important.
If he still refuses, then you start explaining how you will take this to whomever it takes to get it changed, and you will not stop or go away about this.
good luck!