Epaulette Mate

Here's an interesting idea found on Chess.com in a forum thread titled Chess960 Fool's Mate Variation. In the following diagram it's checkmate after 1.e4 b5 2.Qxb5# .

SP921 RKRBBQNN

The thread eventually determines that there are two such RKR***** positions (plus two more *****RKR mirrors). Why two? The Queen must be on the f-file and a Bishop must be on the d-file, because a Knight on that file can block the Queen check. That leaves three squares still to be occupied. The other Bishop must be on the e- or g-file, leaving the last two squares for the Knights.

The thread doesn't discuss the related positions *RKR**Q* and **RKR**Q. In fact, these can't lead to the same mate, because the two Bishops must be next to the Rooks, which places them on the same color square.

All 960 start positions are subject to some sequence of moves -- similar to a 'helpmate' problem -- that leads to the shortest mate for that position. Which positions require the most moves?