I would probably suffer a brain cloud if I tried to do this on
paper.
Anyway, IMO you are either very very close, or else you nailed
it. One or the other.
My pathway to the answer goes:
111111
888
444
777
333
666
222
555
then 5 faces 1 for game.
If 5 wins, it's 6 serves 7 for place, and 2 serves 3 for show.
BTW, in a spec 7 game, post 5 is the highest number to get a possible
4th appearance on the court, so if you ever need 6, 7, or 8 to
win and they haven't done it in 3 times up, you lose.