Sigh. I wish this discussion weren't necessary. But that was... embarrassing. Iron Man had this right, IMO, and I'll go ahead and say I was wrong to disagree with him. Hell, I think half the team should be fired as well, but since you can't do that Mm's going to have to be the guy. You don't take a team that played the Vikings and Bengals tough and lose to the 0-7 2009 Bucs.
With this club, I don't think you want an unproven guy. Just because Tomlin's done well with Pitt, that doesn't mean Frazier would be a good HC - he might be, but then again McCarthy might have been.
Of the 'available' guys, I think it's Gruden, with Mooch a somewhat-distant second - Mooch is too nice, and this team needs Not Nice. This team needs Fear, and Chucky would bring that Fear. GB is a total WCO team, and changing that makes no sense. This team (and its QB) needs a coach they can fear.
If I were Thompson I'd let Mm know that the Dallas game is his GB HC career - and a win will only buy him one more game. Game-by-game - first loss and Capers is installed as interim HC for the balance of the season. Sounds extreme, but the message has to be sent to everyone involved with the team that under-performing won't be tolerated. And honestly, they're at a point now that each additional loss is another nail in the coffin for this season.
Sorry for the ramble - my choice would be Gruden.