Good concept but I think it's cooked. The configuration (in FEN)
r7/1r6/2r5/3r4/4n3/4b2n/4b2b/4b2n w - - 0 1
can't lose as long as you leave one of a8, b7, c6 (or e1, e2, h2) open. Whenever you get a fourth knight just place it on whichever one you left open.
edit: Wait, you actually fit four of every piece on the board, so you don't even need to make any choices.
r7/1r6/2r5/3r4/4n2n/4b2b/4b2b/4n2n w - - 0 1