You need a stuff bag to handle long lengths of rope.Forget coiling. Take an appropriate sized bag and stuff the rope into it, leaving one end easy to reach. To deploy the rope, just pull it out, or toss the bag. The rope will pay out flawlessly.

Doing tricky rappels, I have attached the bag low on my harness, rigged in the normal manner, and gone on down the route, paying out the rope as I descend. I have never had any problems. The same technique works for kayak rescue ropes in throw bags.

I have handled ropes up to 600 feet in length this way. I understand that Yosemite Search and Rescue has a 3600foot length (the height of El Capitan) which is deployed from a duffel bag in this manner.