Lawson Equipment also has high strength dyneema cord http://lawsonequipment.com/. As delivered, it is in a fairly compact bundle.

I also tried stuffing paracord into a small ziploc baggie. The small bag keeps things flat, and the cord can be pulled out easily.

How about vacuum sealing it in a Foodsaver bag? You could tape the outgoing end to the inside of the bag near the top so you wouldn't have to fish for it. The bags are somewhat stiff and when vacuum sealed they should be a little stiffer even.