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I think this is the sacrifice you make with conferences that are too large.  the seven division mates then form the traditional/regional rivalries that the sport thrives on.  And the network gets the content and only negotiates with 5 conferences.

• Your three pod-mates every year
• Your three group-mates every year
• The other nine teams in the conference every third year (host/travel to every six years).  

Three institutions voted no.  The only institution to own up to it for years was IU, however several AD's and prominent coaches were openly against PSU joining due to the fact the negotiations were done very much in secret and only at the president level.  
Delany acknowledged there was "a lot of turmoil" last December over the lack of communication between the Council of Ten and their athletic and faculty representatives.
"I don't think anyone can dispute that. There's been differences of opinion," he said. "Perhaps if we had it to do all over again, we'd use a different process, a process with more consultation. But that's water over the bridge."

IMHO, the pod system fixes this as best as it can be fixed.  
With a Pod system and a nine game schedule you play:

• Your three pod-mates every year
• Your three group-mates every year
• The other nine teams in the conference every third year (host/travel to every six years).  

For fans of each school it would "feel" like you were in a conference with your pod and group mates.  

playing 6 instead of 7 teams each year would be OK
so why not simply put six in a group?  16 or 14 divided by 6 doesn't work

• For Michigan fans, it would "feel like" they were in a conference with MSU, PU, NU, PSU, UNL, and tOSU.  
• For Michigan State fans, it would "feel like" they were in a conference with M, PU, NU, UMD, IA, and RU.  
• For PSU fans, it would "feel like" they were in a conference with UMD, UVA, UNC, M, UNL, and tOSU.  

• Michigan "shares" PU and NU with MSU but they do not "share" their group rivals with MSU.  
• Michigan "shares" UNL and tOSU with PSU but they do not "share" their pod rivals with PSU.  

• Competitive balance:  Each temporary division will have two "helmets" (NE will have M and PSU, NW will have M and UNL, NS will have M and tOSU, SE will have PSU and tOSU, EW will have PSU and UNL, SW will have UNL and tOSU).  
• Scheduling/ticket sales for all:  Each team will play two "helmets" every year.  They will play the "helmet" in their pod annually and they will also always be paired with another helmet in their temporary division.  It would probably also be possible to arrange it such that each team hosted one "helmet" every year.  Ie, MSU will play Michigan annually so they will host them every other year.  Assuming that MSU continues to host Michigan in even-numbered years then I think you could set it up such that they hosted either PSU, UNL, or tOSU in odd numbered years.  The same would be true for all of the Group 2, 3, and 4 teams.  
• No team gets placed in an impossibly difficult situation.  In one example above MSU was in a pod with Michigan, Ohio State, and Penn State.  That would make it extremely difficult to ever win a division.  
• No team gets placed in a ridiculously easy situation, at least not for long.  Last season @ELA  referred to the B1G Championship as the "Badger Invitational".  I know it irked @847badgerfan but the reality is that everybody knew even before the season started that Wisconsin would have to absolutely tank to somehow miss the B1GCG.  Based on this grouping the weakest potential division last year would probably have been SW with 0-9 Illinois, 2-7 MN and IU, 3-6 RU and UNL, and 4-5 IA.  That is bad with six sub .500 teams but that division would also have included 9-0 Wisconsin and 8-1 Ohio State so it would have had a bona-fide championship race and a strong champion (either way).  Ignoring UVA and UNC, the other Division, the NE, would have had a great Championship race between 7-2 PSU, MSU, and NU along with 5-4 contender Michigan.  

• Michigan:  THE GAME, no more needs to be said.  
• Penn State:  Border state, traditional "helmet", this is great, IMHO.  
• Nebraska:  Lincoln is FAR away (I know, I drove it) and obviously the Cornhuskers are not a historic rival but they are a historic "helmet" and I like this rivalry.  
• Illinois:  The Illibuck trophy.  Nobody outside Columbus cares but up until a few years ago Illinois was Ohio State's longest-running annual series.  Illinois is Ohio State's second most frequent opponent and the only team other than Michigan that the Buckeyes have played more than 100 times.  
• Indiana:  Border State, easy to get to away games (the nickname "Horseshoe West" is apt when Ohio State visits Indiana.  

Note for @TyphonInc  :
I know you hate this and I understand why but I disagree about getting "saddled with" Indiana.  Indiana hasn't typically been very good but they are a border state and the games in Bloomington are easy for Ohio State fans to get to.  IMHO, the only every-year opponent for Ohio State that I wouldn't be happy about is Rutgers.  The others:

• Michigan:  THE GAME, no more needs to be said.  
• Penn State:  Border state, traditional "helmet", this is great, IMHO.  
• Nebraska:  Lincoln is FAR away (I know, I drove it) and obviously the Cornhuskers are not a historic rival but they are a historic "helmet" and I like this rivalry.  
• Illinois:  The Illibuck trophy.  Nobody outside Columbus cares but up until a few years ago Illinois was Ohio State's longest-running annual series.  Illinois is Ohio State's second most frequent opponent and the only team other than Michigan that the Buckeyes have played more than 100 times.  
• Indiana:  Border State, easy to get to away games (the nickname "Horseshoe West" is apt when Ohio State visits Indiana.  

None of us are going to get everything we want so I'd be thrilled with five out of six of Ohio State's annual rivals making geographic, competitive, or historic sense.  

Honestly, I think the two schools that get screwed the most in this hypothetical set-up are MSU and Iowa.  They get stuck with two eastern schools (RU and UMD) in their group.  Everybody else only has one.  

@medinabuckeye1
I don't "hate" getting saddled with IU, (even in my geographic pod scenario, I had IU and Ill in OSU's Pod.)

But, I don't like having 3 cup cakes as OSU permanent Pod mates.