Another solution which puts the onus on them, is custom fields.
Get them to fill in a custom field during registration with a list of teams. They would need to update this themselves if things change. It can be a drop down list of teams.
When using the Email Users function, you can filter the users the email is sent to by a custom field value.
Thread in team 1 is updated, send an email to all users who have a value of "team1" in their team custom field. Or, promote to specific user groups based on the value of that field, and send the email to that group.
I appreciate you can't necessarily rely on people to put the correct team in, nor update it if that changes, but I would guess the same is true for them watching the correct thread/forum.
Though it does solve another problem. If teams change, currently, I guess they need to remember to unwatch the current team and then go and watch the new team. If they can only specify one team (or a multi-selection of specific teams) then that step should be easier for them. It's also basically zero effort for you as a busy admin to manage too.