Marc, the furling idea might work, but would rely on more skill and luck than I possess, compared with simpler recovery techniques.
The main difficulty would be trying to uncleat BOTH the lines from your lower position in the water. The cleats are going to want to lock from all the down pressure. Being dragged through the water, it would be especially difficult to release them. If you dismounted between the Akas on an AI or TI, matters would be worse.
But suppose you managed to get both lines to stay uncleated, would you have enough leverage and control in the water to furl a powered sail? Uncleating the furling line in heavy wind is likely to release MORE sail.
And there's a chance that a cleat would break or dislodge from the crossbar. Not likely to happen to both cleats though.
I believe what you really want to do is get the sail to luff, rather than furl. That will slow the boat and buy you time to hop on board. Try this first -if you can get it to work, then you are on the right path.
Attaching a short quickrelease harness or surf leash to the sheet seems like a good idea. Not as reliable as an Aka member, but it would provide extra freedom of movement and tend to turn the boat, should you be pitched. Hopefully, you can keep all the lines from fouling during normal sailing. (Note: I keep a death grip on sheet anyway so I rely on that and my leash for safety).
My brain can't handle complex tasks even when I'm dry, so in a MOB situation I need to focus on as few priorities as possible. I have concluded that those are:
1. Making contact with the boat.
2. Getting control of the rudder (by hand)
3. Depowering the sail. (luffing or any means possible)
Furling the sail is worthy goal, if you can manage this while wet. Anxious to hear how it goes with your test.