Well, immediately after my No Refunds run, I had a near-perfect House of Pain, and figured I'd post it here since I'm unlikely to do much better (from a numbers standpoint).

It's a min kill run (excluding the 3 Reapers that popped, and I can't do anything about that) and includes ONLY the kills from the last fight. Everything else was stealthed or otherwise bypassed. I got unlucky with a Reaper during the rats/valves section, and pulled some rat aggro (but I escaped without killing any rats, but did kill the Reaper) which made it imperfect from a 'no aggro' perspective, but otherwise it was as good as could be hoped. Two additional Reapers popped in the last fight, so theoretically the absolute minimum is 36 kills.

Enjoy!