It has already been addressed by other comments in the thread that there are technical and possibly other concerns with various methods of attempting to identify multiple posts in the thread as having the same author.
If that is set aside for the moment, then (continuing with the idea) the next option would seem to be to keep track of the number of posts by the anonymous monk and denoting them much as described in the OP, so that if post N in the thread is the first by an anonymous monk it is labeled as by AM-1, post N+1 labeled as by AM-2, and so forth. Unless they reveal themselves as being the author of a previous post in the thread, however, you cannot be assured that the posts by AM-1 and AM-2 are actually separate instances of the same anonymous monk.
Alternately, one could just refer to the posts themselves (as they can do currently). You still don't know for sure if posts by multiple anonymous monks are by the same author, but you know for sure which post to which you are referring. And isn't that the important thing, the comment of the post-not the author? (Important enough it was a monk's signature line, although I cannot recall whose at this moment.) In theory, we up/down-vote directly on posts based on their content, not the author who wrote them. Also in theory, those monks with greater experience have contributed more to the monastery, and those with higher experience to writeup ratios have contributions that may be held in slightly-higher esteem among their peers here.
Just a thought. (It was free, and no electrons were harmed in the construction of this post.)