Yes, I use the rings you despise.
But once I have them in the ground I really never have to move them again. I only move them if I need to move the peony. When I cut the peony back in the late fall, I push the ring back down a bit farther into the dirt and then in the spring as it grows I raise it. It works for me.
Yes, you are correct in deadheading your peony, unless you want it to set seed. I don't and so I snap mine off too when the bloom is finished.
Most of my peonies are pretty much done for the year. I was out tonight deadheading away.