HOLD ON... there is hope yet! After countless attempts to get into public games tonight I just played a game on The Giant. It was 4 players, and the host quit on round 18. BUT, after a short delay the host actually migrated! Took a while and I figured the game was just going to end, but we ended up making it to round 21. Even better, low and behold there it is on the leaderboard... round 21, counted as a 4 player game!
Praying that you just got unlucky earlier and Treyarch has indeed finally made the leaderboards behave the way we all want them to!!! Makes me think back to all the long nights in BOII wasted when someone would quit a round before my personal best. Could be a dream come true here... now just get your damn servers working, because i've yet to make it into a public game on Shadows.