I'll admit to being confused here. Are we talking about a simple pigtail? I'm not sure what is being described with the ring and sucking up spin sheets...
At the clew, where the sheets attach, you tie a small piece of line with a ring on the other end. Your snuffer line will then go through this ring before it goes through the snuffer rings/grommets on the spinnaker. Now, when snuffing and the sail bunches up, the clew will be at the bottom of the ball of spinnaker fabric as it goes into the hoop. When snuffed, it will draw in 4 to 6 feet of each side of the spin sheet since the clew is now nearest the bottom of the snuffer sock instead of right at the opening. It does require a slightly longer halyard/snuffing line.
In some cases, this can make launching the spinnaker easier if you have a very resistive launching system. I've also seen it make launching tougher...user experiences will vary.