Hi, Andrew,
The two lower barrels are wound by the gear in the center (three gears at the top in the picture) - the crown winds bi-directionally, one way for the timekeeping, the other for the sonnerie.
I have heard of some attempts to run the sonnerie off the main timekeeing barrel, but that is very impractical/dangerous. More than two? I haven't heard of any.
In Grande mode, the AP and the Dufour give about 8-11 hours (remember, there are an awful number of strikes during this period, as each quarter it needs to strike the hour, and the twin tones of the quarter x the quarter.) And of course, striking the repeater on demand depletes the sonnerie power reserve even more. I suggest winding every 6 hours or so; inevitably, the sonnerie is completely wound down by the late afternoon (assuming one winds in the morning) - just in time to be asked to demonstrate the repeater on demand, and get nothing...
;-)
It's a wonderful specialty area.
Cheers,
TM