[violetpretty]

Get recs through your own networking first. Then go to APH to fill in the holes, and when you request recs for the ones you are missing, make sure you emphasize that these are not necessarily your top choices, just the ones you don't have a rec for.

That is really weird about saying, "Ok, pick X number for us to write recs". They must have more than that number represented if they're asking the OP to make a choice.