Ok, I do enjoy the speculation, Id bring Sibley in how they introduced Cook, at 3. Team:
If Broad sorts his head out against the quicks, bump him up the batting order. I think a temporary spell with him as captain would free up everyone else to play and let an alternative captain for the future develop. Probably Burns if he can become an automatic pick.
I would also have any spin coaches available to help learn how to set proper fields with the captain, leadership and bowlers. Roots fields to spin are always a bit off.