"...I'm pretty sure it's A, then D, then A,..."

That may well be the case when I think of it. Mick has a high range, and a few of his songs test the vocal chords and the lungs to their limit.

He would therefore have capoed at the 7th fret.

I have a tendency to bring the key down a notch or two, which is why I would have said the 5th fret initially.

B.