You DO NOT have to have an even number of teams to run a league in a head to head format.
If you run through CBS or any server that allows multiple games per scoring period, you can customize a league schedule so that some teams play 2 games in the week while everyone plays at least 1 game.
1 v 2
3 v 4
5 v 6
7 v 8
9 v 10
11 v 1
2 v 3
In this case, youd have 7 games in a week so 3 teams would play two games (teams 1, 2 & 3) and the rest are playing 1.
The next week you schedule it so 3 different teams are playing 2 games.
This eliminates the need for a bye week.... this of course if you can't find a replacement. The point is, you CAN do it.
Writing those kinds of schedules can be tricky, but it can be done.