Ralph,
I never disconnect the shrouds from the mast or the boat so the rings are not an issue. I tape the rings on the shrouds to be sure they don't come off. When I lower the mast, I coil the shrouds and hiking wires in loops that I tie to the tramp. When I raise the mast, which I do alone, I tie an 8' line from the jib halyard to the bridle and rest the end of the mast in tripod. I raise the mast and, while leaning into it, reach down and undo the jib halyard. I pull in the jib halyard until the mast is supported and tie it off on the cleat. I then get down and fasten the forestay. I reverse the procedure to put it down. The only ring I have to work with is the forestay and I have all the time I need. If you have to remove the mast from the boat each time this won't help you.
Howard