Played a lot of games here but I'm pretty sure I did try this. Also pretty sure it didn't work at all. The engine won't look at your players F to K, it will simply try to play M when your starters tire, and because he can only fill one position, your starters will just get tired. Likely M will play two different positions in each quarter if you have players with different levels of stamina. I think its probably not predictable which two positions or even if they'll be the same positions in each quarter.
Great idea by the way, and really exactly how I'd like to the game engine work.