Chris Woakes, eh? 11 wickets in the game so far, and you would bet on him making it a round dozen or more. And he was the third highest scoring batsman in England's first innings, with a very handy 35 n/o on a difficult surface. If England drop him to make way for Stokes, they are beyond redemption. If you find two serious all-rounders, play them both; Stokes as a bit more of a batsman, Woakes as a bit more of a bowler.
So then, let's review our current 11 of choice:
Cook*
Hales
Borthwick
Root
Bairstow
Stokes
Buttler+
Woakes
Rashid
Broad
Anderson
For me, the leg-spin pairing of Borthwick and Rashid seems more promising than the sedate off-spin of Moeen Ali, and they provide as much batting. Borthwick's inclusion at 3 also affords Root a bit more protection. Buttler needs to be in the test team, in my opinion: he is one of England's most naturally talented batsman and a star in limited overs formats, and his wicket keeping is more reliable than Bairstow's.
This line up, at its best, has 9.5 recognized batsmen, a 6.5 man bowling attack (Root's offbreaks are serviceable enough), and a reserve wicket keeper.