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Would every team claim a divisional crown?

PJ Barnum would have "co-champion" rings made, like he did in 2019.

In the B1G-E wins by tOSU and M thus weekend would mathematically eliminate Indiana and MSU and possibly Rutgers while practically eliminating everyone except the Buckeyes and Wolverines. 

well, the big ten schedulers didn't give Bert much of a chance to win the west back at the time

I get it but I still think it was silly to take the chance.

Indiana/Purdue is different. The Hoosiers and Boilermakers have played for the Old Oaken Bucket the last week of the season almost every year since before WWI so there is a lot of history.

Additionally, Purdue and Indiana are two of the least successful football programs in the league so the chance of either one making the CG are remote. The chances of both making the CG in the same year are vanishingly small.

Michigan is the second most successful football program in the league within their period of contiguous membership. It shouldn't be hard to forsee that they might make a CG run once in a while.

Illinois obviously has less historical success than Michigan and their overall record is bad enough to be comparable to Indiana and Purdue but Illinois is a strange case. For a program with such a bad overall record they have a surprising number of league titles. This is because Illinois' history has been a case of feast or famine. They are rarely mediocre. Historically it has been mostly awful with an occasional dose of really good thrown in.

I suppose they could always play all conference division cross overs early in the season.

This!

I would minimize crossovers late in the season which they did.

The problem is that each division has an unequal number of teams so in order to play a full slate of league games there has to be one crossover game.

To minimize the chance of a short-turnaround rematch I would not allow the historically best teams from either division to have a crossover game late. Thus my solution with this year's matchups would be:

• Final weekend, November 26: Purdue at Indiana
• Penultimate weekend, November 19:  Rutgers at Minnesota
• Third-to-last weekend, November 12:  Northwestern at Maryland
• One month out, November 5: Michigan State at Illinois

In this way the likely long-term top-3 from each division would not play any crossover games within a month of the CG.

• tOSU, M, and PSU from the B1G-E finish crossovers in October.
• UNL, UW, and Iowa from the B1G-W finish crossovers in October.

Even for the other four in each division:

• IU, RU, UMD, and MSU from the B1G-E play only one crossover in November and it isn't one of the historically best programs from the B1G-W so the chances of a short-turnaround rematch are miniscule.
• PU, MN, NU, and IL from the B1G-W play only one crossover in November and it isn't one of the Helmets from the B1G-E so the chances of a short-turnaround rematch are miniscule.

I would set it up for 2 teams, 1 from each division, to get a bye the 2nd last weekend.  Make sure those 2 teams are playing week zero games so that they get 2 bye weeks in a season. 

That is a good idea. I didn't want any byes that late but I hadn't thought of compensating by having them start a week early and get two byes. All you need is an annual crossover in week zero.