Yep, people are already making them:

https://fruitychutes.com/uav_rpv_drone_recovery_parachutes/m...

Maybe. I'm no aeroE, but I know parachutes need a reasonable bit of space to deploy. I'm not sure the quadcopter would be flying at a high enough altitude to be able to deploy the parachute, have it unfurl properly, and then contribute enough drag to slow the craft.

Also, it'd mean either parachute or this failsafe rotation technique. Spinning freakishly like the video shows would only get the quad entangled with a parachute.

Sure but you would need to cut the motor immediately, otherwise you risk tangling the chute. Not to mention the point of this fail safe is to allow the pilot to get the quadcopter to a better spot for landing instead of crashing in to a tree or something terrible.

What do you mean by "keep the fly time mostly intact"?