Barry and McCarthy both played the full 90 minutes against Liverpool at Goodison last year. Think the only times Barkley was one of 2 centre midfielders last season were against City the first time (Barry was ineligible), and against Palace the second game (paired with Barry in central midfield first, then paired with McCarthy when he came one, and they sliced through us like butter all game). I'll give you the QPR game though, he was immense there.
I agree he plays well when he has space in front of him, but I think the best way to create that for him without exposing ourselves is to play him in a 3 man midfield in a 4-3-3. He should play alongside 2 of Barry, McCarthy, Besic, and Gibson, and behind 3 of Lukaku/Kone, Naismith, McGeady, Mirallas, and Lennon. That said, it looks like Martinez intends to use Gibson further up the pitch than Moyes did, he almost looked like a #10 against Leicester and Young Boys, so we may see less of the 4-3-3 and more of Barkley out wide (which I know GOT will just love).