This is a really good discussion... I'm squandering too much time at work thinking about this!
I'm a little old school and reluctant to change on this. I love the conference tourney as an event, but hate it as it relates to producing a meaningful award (outside of the auto-bid for NCAA, which is fine). Regarding the notion of 2 champions, I'm certainly of the opinion that 2 champions of the same league for entirely different purposes is dumb. If it were up to me, the championship would be the prize for the regular season, and the only award for the tourney winner would be the auto-bid (unless a better prize idea came to be), much like it is today.
But I do respect that that view is not held by everyone. And it would seem that this sillyness of a championship + a tourney championship has to end at some point. So if there someday can only be 1 champion... I will say there is an element of cool to giving the championship to the tourney winner, to me at least, but that's probably driven only by my love for the event (re: thinking with my heart instead of my head). It would definitely be an exciting way to award the title. The practical side of me says that route presents a greater risk of doing a disservice to the B1G championship than the inverse. For example:
1 - IU is the 1-seed this year. Suppose Purdue is a 4 and Wisconsin is a 3 (just making these up). If IU doesn't win it, and instead it goes to Purdue or Wisconsin (or anybody for that matter), how much damage is done to have proclaimed IU the B1G champion? Some, for sure, but a lot? But should 1 loss in the tourney undue the body of work that is the regular season? For objectivity sake, try to ignore the fact that it's IU in this year's #1 spot
Let's pretend Purdue is #1.
2 - Conversely, imagine if the champion on record was solely based on the tourney championship. Again, pretend Purdue is the regular season champ and #1 seed. And in comes lowly Nebraska or Northwestern to win the tourney (perhaps Purdue gets knocked out by a good team, and that team blows a game to to Nebraska in the final). They'd finish the year with barely a .500 record AFTER adding in the tourney wins, yet they'd be declared the official champion. Then forever you look back at the record books and each time you see Nebraska in 2016 you're like "Nebraska... that's weird... oh wait,
now I remember".
It just seems to me if you had to pick one of the 2 above, you'd have to go with #1 because it would the lesser of two evils. Sure, imbalanced deludes the title race a little, but not nearly as much if an 8 or 9 seed were to win the tourney for some dumb reason and be declared the league champion with a 7-11 record or something.
As an alternative though... if I were in charge I might consider an alternative hybrid model that gives the official championship to the team with the best record
after including the B1G tourney results. This is attractive to me because it pretty much ensures one of the top 4 or 5 teams in the regular season gets the title because lower level teams couldn't amass enough wins in the tourney to beat the better teams' records. Another benefit would be that because of the byes and double byes, different teams will have different number of games played, which would inevitably reduce some of the craziness with tiebreaker scenarios.