Schwartz is the DC of the Browns.
Even if he were canned by CLE, he might not get an interview with a team like GB after his shenanigans as the DET HC back in the day.
Agree Barry has never done it, which isn't a great predictor that he ever will. He's had a few years with GB now, with a good amount of talent, and has been middling at best. IIRC this is the last year of his contract, so I think they'll give him the Pettine treatment - not renew the contract as opposed to firing him. Someone will likely shake loose at end of year who is a better candidate to take over. I hope.
One thing that would need to be a consideration is not making such a big change that your players don't fit the new scheme. There are probably some Staley/Fangio acolytes that could do as well as Barry who will be available.
Maybe Staley himself if Chargers keep struggling.
Ring the bells that still can ring
Forget your perfect offering
There is a crack, a crack in everything
That's how the light gets in - Leonard Cohen