We carry a small fabric drogue in our tramp pocket and deploy it when the capsize is problematic - first and foremost if one sailor doesn't manage to reach the boat, but also if we don't manage to turn her head to wind by sitting on the bow, or when to close to rocks.
We have a long 6mm line attached to the capsize line, and initial deployment stops drift. We then tie the drogue to the bridle, and from that moment she lies quietly head to wind, almost no drift and plenty of time to prepare, overturn, climb aboard and even rest before reeling the drogue in and sailing on.
For our new boat we are considering sewing a dedicated drogue pocket on the bottom side of the trampoline.
I like the idea of a strap there to reach the rudders, we're adding that as well.