I've seen your page before, but the thing that has confused me about
it and especially that circulation diagram is what would happen to a
tab-style stall warning device installed at the front of the wing in
that diagram. Wouldn't it be going off all the time?

The diagram doesn't show the flow at fine enough scale to infer that
kind of thing. Even though there is a general upward movement of air
ahead of the wing it isn't a clockwise flow relative to the wing.
There is a line at the leading edge called the stagnation line. The
air that hits the wing above this line goes over and the air below the
line goes under. As angle of attack increases, the stagnation line
moves back and down. At high angles of attack, it can get far enough
back that air does flow forward across the wing. This lifts the stall
warning tab and sets of the horn. This is related to but is not the
same thing as circulation.

--

Roger Long