Yes, in this play.

But, I meant that last toungue-in-cheek comment more generally.

A2 launches a try. The horn sounds. The ball hits (a) the backboard or (b) the floor and then enters the basket.

Ruling?

I know what we'd all do (count it / don't count it), but the wording in the rule ... ;)

I agree with this interp. Just insert "ball bounces back to player" after "hits B's rim." That is where your second dribble starts but I wouldn't call it until A1 touches it again.