Daddario XL regular light gauge, regular scale length strings on both my mustang PJ. No flop here.
I found the same. I personally don't like the sound, but they definitely feel a little stiffer than all the other short-scale strings I've tried.
Floppier:
LaBella Flats (Maybe they are flexible, but higher tension?)
LaBella white tapes
Dr Sunbeams
Original Fender strings
That said, I didn't find any of them to be a problem. The white tapes in particular require a soft touch, but if I want to dig in at all, I play a little closer to the bridge. If you play in front of the p pickup, everything feels floppy. I think Joe is right about changing technique.