Cool idea. I found a way to make 15:

q6Q/q5QK/q3k3/q7/q7/q7/q3N3/bQQQQQQ1 w - - 0 1

I’d be interested in versions with only reachable positions. https://en.wikipedia.org/wiki/Proof_game

What if you combined your final version with your interleaved approach to add the last two queens? I’m not sure what would be required to remove ambiguity, though.