Hey Ted,
I have started to break up the groupings I have found by splitting out the unconfirmed examples to see where that gets me. As you noted there are several cards that are unconfirmed across many backs....one could assume these are a grouping that likely don't exist in those f/b combination...however I am hesitant to go to far down this path as it can cause more uncertainties if one does show up...like the three examples with OM you listed.
There is also the potential that during a second/third print run that a player was swapped out (error, team change etc) on a sheet and that sheet then printed with a back that the initial sheet wasn't.
First print run
Sheet of 10 cards printed with Piedmont & Sov backs.
Second print run - card 10 is swapped with a new card
Sheet of 10 is printed with Piedmonts backs and now an OM run.
You end up with
11 cards with Piedmont, 10 with Sov and 10 with OM and the two cards that were swapped have different f/b combinations..one has Pied & Sov and the other has Pied & OM. This really messes the groupings up as they appear to be in separate groupings even though they are sheetmates to the other 9 cards.
I think it will take a group all working together with the pop reports and everyones data to really solve these once and for all.