Came up with a draw scheme (see attached image, red or blue can be chosen to represent home games, it doesn't matter which). Start off in round 1 with team 1 vs team 21, team 2 vs team 20, team 3 vs team 19 etc. Then proceed to the next team in order each week. Use team 22 as the "bye" team for when each team runs into themselves in the pecking order (black squares in the image; team 11 in round 1). Home games alternate each week nicely. The weeks before and after playing team 22 will be opposite (1 home game, 1 away), meaning there will be a double-up for each team one way or the other. An even number of rounds can be had by repeating rounds 1 (for 22 rounds), 1-3 (for 24 rounds), or any arbitrary rounds really, with the home teams swapped. The final step is assigning team 22's home games such that each team has an equal share.
Example: teams 1-10 assigned home games in round 1, round 1 repeated as round 22. Teams 1-10 will end up with 10 home games and 11 away games, so their games against team 22 will be at home (even rounds). Teams 12-21 will end up with 11 home games, so their games against team 22 will be away (odd rounds). Team 11 will play team 22 twice. Assign 1 each way as desired.
I've gone with the same team numbering as Mis, meaning the Churr Bros are the "bye" team. Their row and column is magenta because their home games are determined after the number of rounds is decided and which rounds are repeated.
