This is complete speculation, but here's what I would want to do:
1. Have an hour-long Barker episode on hand which shows Bob at his best.
2. Preempt the day's scheduled episode and air the Bob episode instead.
3. Don't do anything in-studio, because whatever episode that's next to tape will air weeks after the fact, and it's going to look awkward.
I recognize that there are behind-the-scenes hurdles to be cleared for this plan to work. But I agree that a new "Salute to Bob Barker" episode, no matter how quickly they're able to put it together, would come across as tacky.
Of course, since we're discussing what the show will do... Again, this is speculation, but I'd put my chips on "Have Drew say a few words at the beginning of the next episode to tape, then put that episode on the air as quickly as possible, preempting the day's scheduled episode." Maybe with a side bet on "Drew tapes a 30-second tribute alone and they graft it onto the beginning of the next scheduled episode." I don't think they will or should make it an all-episode affair.