Is there a way to limit how many of a certain piece are on the map at the same time?
Not exact the answer to your question but,
"At-Start stack" to add only the number of pieces you want,
and not the 'Game Piece Palette',
and don't put 'clone' on the pieces,
That would limit the total number of pieces in existence.
I don’t know of a way to limit pieces just on a specific map, if there are more in existence. But I am new at VASSAL programing.