I took biochem the semester prior to my MCAT studying, and really think that helped my studying and final score (131 in biology/biochem section). Just from my experience, I think teaching yourself biochem is an option, but not really a smart one. The topics are fairly complex compared to other pre-reqs, and it'd be difficult for anyone to fully grasp them without some form of lecture/lab. There's also so much biochem on the exam like you mentioned that the effects of self-studying will be magnified, to the point that it could potentially hurt in the end.
Bottom line, you might self-study biochem and find that you do well and get a score you're happy with. But, I'm willing to bet you'd score higher with an actual biochem course under your belt. Or, you may find that you don't score as well as you'd like and wished you had just put your MCAT off to take biochem. I agree that your situation is kind of unfortunate, but make sure you're willing to risk a potentially lower MCAT score.
EDIT: Someone in pre-allo just asked virtually the same question, so I pretty much just copied and pasted my response from there.