What if the Character page had a checkbox beside each name, indicating the player’s willingness to participate in Dom with that alt that week?

The checkbox’s state could be set in stone as soon as the player gets a scoop that week, and only a set number of boxes per week could be set before you could move from the page.

This way, if the alt limit is raised or lowered, there’d already be a framework in place for dealing with it, and the player would be required to maintain his or her alts, instead of letting the server guess who gets to play in a given week.