I come from a huge school as well. Just think of having chem and orgo in a 500+ lecture hall. The class had around 800 or so students (there were two sessions a semester). So, needless to say, I can't go to my instructors for rec's. Here is how I weathered this dilemma:
1) I did research in a great lab where I interacted with the principal prof and the other assistant prof's in the lab. I got a rec from the main prof who emphasized my research and "scholarly" potential, and another rec from an assistant prof who supervised me on a daily basis...she wrote on my "character." I didn't have access to the letters, but explained to them this is what I wanted emphasized.
2) As for how I do in class, the only prof who I had some sort of interaction with was my faculty advisor (who you talk about your schedule with). He spoke about my academic record.
My school has the premedical committee system, where you pay them an exhorbitant fee so that they write a letter for you. They basically assign a random faculty member to interview you, and then write a rec pulling together the interview impression as well as impressions from the three people mentioned above (you submit three recs to this committee). Then, it's stamped with the university seal and mailed to whatever med schools you want.
This is how the "premedical committee letter" worked. Plus, they put a cover letter explaining how the classes are structured here. Check with the career office/premed advisor at your school.
This system worked beautifully for all schools except one, which required two letters from instructors. I gave them the premed committee letter with all the add-ins, and then scrambled for two TA's who taught sections (small groups) to write letters for me (since my school is so big, that's the only meaningful interaction I had with instructors).
And, I survived
Some other advice:
It helps to get a faculty member
It helps to get an MD
But, a TA is good too, if you have at least one of the above.
Choose people who know you fairly well, and who you are SURE will say good things about you. What I didn't like about my school's premed committee format, is that the random interviewer can pretty much tip the scale for you (in my case, not so fairly)
good luck!!