Been thinking about this. Taking another crack at it, somewhat seriously.
CB: Keane (or anyone but Williams)
LB: Martina (please come back, Baines)
CM: Sigurdsson or Rooney (Rooney much better for passing from deep but we can make either work... maybe)
Defense mostly picks itself (Holgate's partner -- what to do?). Gana is there to stay put and tackle/intercept everything that comes near him, his best role. Davies and Vlasic are there for ball progression (via dribbling) and retention (both decent at holding it in tight spaces) and also winning fouls. Walcott, Tosun, and Sigurdsson/Rooney are the "finishers," the players we need to make the final pass/shot.
I went for Vlasic over Bolasie/Lookman because, while those two are unquestionably better dribblers, they're also total wild cards who are just as likely to give the ball away as they are to pull off a bit of magic. Vlasic isn't as explosive but there's a premeditation to his game that those two lack and that's what I want in the team. He doesn't need to do anything special, just hold off pressure and help us inch forward.
Probably still shit but that's what you get when you buy a bunch of individuals with no regard for how they fit together. It's hard to find a way to get from defense/midfield to the final third, as evidenced by the fact that I'm hypothetically asking Davies and Vlasic to shoulder a lot of that.