For the rotation and casual I would suggest a pretty opaque "Quick Match" option.
Based on available players it goes through several pools of options, no option is solo.
- 6+ matchable players: Regular but easy Teamgames, Mini Dual Gap?
- 3+ matchable players: 2v2, 3-5 vs. AI
- 2 matchable players: 2 vs. AI, short campaign missions
I think the Player Councillor should play a big role in identifying popular and disliked options for the "Quick Match" matchmaker, and act quickly if needed or opportune.