That's how i started a deep, and i take it it is deep, 22m socket onto a plastic hexagon that is what remains after the handle has been taken off.
It is a deep socket isn't it?And it is attached to the drill via a drill driver that fits into sockets.
Your findings with the drill are correct, slowest speed on the drill setting.And you have identified the two other problems, the snatch you get that might break your wrist, and the potentail to strip the plastic hexagon round.
I did use it successfully like this for a fair while.Other people tried and found that the snatch was to severe and gave up.
Depending on which way you are winding in i laid the drill on a box so that this took the force and not my hand.
Eventually i put a dog leg clutch on which allowed the reel to continue to spin.The principle of this is the same one as car starter handles.
After about a year the reel innards wore out, because they are plastic. I bought better reels with metal parts and rigged these up to work,The old reel has been refurbed with metal innards and is now my spare/third reel.
If you want to pursue this it's not cheap, but the benefits are worth while.