The following IS NOT an endorsement, just some info I have not seen posted...
The first REAL coaching job Mike Bajakian got was at Central Michigan as a QB coach under Mike DeBord in 2002-2003.
Bajakian then went to the Chicago Bears as a Quality Assistant from 2004-2006, before joining CBJ at CM as the OC.
He's now back with Lovie Smith at Tampa Bay.
DeBord also coached for the Bears and Lovie Smith from 2010-2012.
In DeBord's first run as OC at Michigan, Brian Griese was the QB in year one, with Tom Brady being the starter for the rest of his tenure. According to his wiki he was 52-11 as OC in that run. In his second stint he had Chad Henne with Ryan Mallett as a back up.
Obviously, the offense Bajakian has been running the last two years shares little resemblance to the Michigan Offense we saw under Carr and has nothing to do with what Bajakian would have been seeing working for the Bears.
This implies that he learned the offense that Jones wanted to run from Jones. That does not mean that Bajakian didn't bring terminology, blocking schemes etc... to the table and all of that would be at least somewhat, if not very, familiar to DeBord.
I don't think CBJ is willing to scrap the past two seasons and start over and if there is a guy out there that can come in and continue what he's started, I think CBJ would find that invaluable.
As previously stated this is not an endorsement of DeBord, just my guess as to why he's a candidate.