The best way to do anything bigger than 10 is to have one protected (rivalry) game for each team then rotate the rest of the teams so you don't play anyone more often than anyone else. Otherwise if you try to split the conference in half or pods you end up with continually unbalanced schedules like what happened in the old Big 12 North & South and the current Big 10 & SEC.
Yeah, there’s really not a good way to do it. The B1G couldn’t accomplish anything
close to a balanced schedule, and they only had 14.
When you’re trying to protect rivalries and at the same time balance the schedule/get all the conference teams to all the schools eventually, it’s really hard, if not impossible. This idea of one rivalry game per school and then just rotating through the rest of the conference isn’t terrible, as far as meeting the criteria - but schools almost always have more than one opponent they’d like to play every year, and that doesn’t fit this model.
The other notion - which doesn’t help with the “play a variety of teams in your conference” - is to just accept the reality that 16/18/20+ conferences aren’t “conferences” at all, but (at least) two separate conferences with an agreement on a common champion. Just split up your divisions into nine or ten schools, then your conference schedule is simply playing the rest of your division. No, it’s not balanced, but what else are you going to do?
Every schedule that’s not a true round-robin is unbalanced to some degree - pods don’t help that, rotating through the whole conference doesn’t help that. Just agree that your two division winners play for the championship, and that’s that. (Or have a four-team playoff if you’re really broken up about a team that couldn’t even win its own division possibly getting left out of the CFP … /stares at SEC/ …)
Maybe mix up your divisions every couple of years, so you can get schools to see everybody else over time. Again, though, that plan would affect your set “rivalries“ - you just gotta decide what’s most important.