Actually, the obvious person is Ali. He has a good record as a one day captain: alternatively. Root should be asked to stand in for one test. If Foakes was unavailable, the other Ollie Robinson (the one without historical racist tweets and fitness issues) should be given a chance. Kent were mad to let him go, but they've made a lot of dubious decisions re wicket keepers in the last twenty years or so.
I would agree with Moeen Ali. It clearly would only be a temporary arrangement, and as you have mentioned he has captained the one day side in Buttler's absence.
I don't think that I have ever read anything about the suitability of Bairstow as captain, perhaps he is one of those who would never want it neither would I bring in anyone who is not in the team....remember
Chris Cowdrey anyone? Brought in as captain because he had an England legend as a father and was godson to the chairman of the selectors, Peter May. 1989, I think, when England had 4 captains in a series
(if my memory serves me well!)
...but let's hope Stokes can pull through.