For the third test, I'd go for:
Compton, Cook, Bell, Root, Bairstow, Stokes, Buttler, Ali, Woakes, Broad, Anderson
I'd put Compton back in for Lyth, never should have been dropped in the first place and we actually averaged 50 as our opening partnership with him around. Not a long term option or exciting but the kind of person need with Cook to set up an innings.
Last chance for Bell, really only keeping him in as its his home ground, and despite his awful, awful form, he's at least not getting out to the same glaring technical weaknesses like Lyth and Ballance, but being completely incompetent is scarcely better. Bairstow for Ballance is a pretty obvious one, not sure he's up to it either but his form warrants a chance, and Ballance just can not handle Australia's bowling, that's not something thats going to change.
Finally I'd have Woakes in for Wood who looked tired, though I do like Wood, Woakes on his home ground would be a shrewd move and though he hasn't played much since his injury, he has taken wickets at a good average in both his county games so far.
The absolute worst thing England can do is keep that top order the same, which is what I suspect we will do and will lead to yet another 30/3 scenario.