I was assuming the tempo was like what Alistair Anderson uses for triple-time hornpipes. Dunno what kind of dance he's expecting.

Bb is the way Purcell printed it. It's common for Baroque string music, and Abdelazer was for strings and harpsichord as far as I know, so brass doesn't come into it. G minor (or G dorian) is even more common, and stayed that way into the middle of the 18th century. I've never figured out why. It's easy enough on the recorder but a bit of a bugger on most other instruments of the time, and the recorder wasn't a big enough deal to decide the choice of key very often.

I suspect the string groups you've heard doing it in A are actually doing it in Bb at A=415.

Looking the score for the complete suite, the key sequence is pretty logical: Dmin, Dmin, Dmaj, Gmaj, Gmaj, Gmin, Gmin, Bbmaj, Bbmaj/Gmin. And there are only 3 notes out of first position on the fiddle in the whole score, so maybe it's not that hard after all.