Check airman should bid like all other captains. The trips that they can hold by regular seniority get pulled from the FO trip pool like they do for the no-fly list trips.
Yeah, getting the trips bought from the FO would be great, but this at least solves the seniority bypass on the captain side, without messing up the FO side extra.
Yes, I know, it's not in the contract, but I can dream can't I?