Can anyone point me to a reg cite (or AC, or FAA legal interpretation) that spells out which Part 121 checking events may also serve as a Flight Review?

FAR 14CFR 61.56 (D). Refers to a PC conducted my a company check airman

14 cfr 61.56

Ok, so what is the official definition of a proficiency check? Which AQP event counts? The MV? The LOE? A line check? And what evidence could I show of one?

The LOE is the official "jeopardy" event, so I would use the date of the LOE. A line check is not a proficiency check. Evidence would be your company training records.

As far as what counts under AQP it's depends on the MOU your company has with the FAA CMO that oversea's the company. It's not the same for all companies. Your training department should be able to answer this question.