Ok, I've read a ton of things about HB eggs over the years, and make them a lot, and a lot of it is inconsistent. Regardless of method (I used to make them like you do with the lower heat after boiling, but now I'm back to just boiling them for 8 minutes with no difference and less steam in the kitchen), I usually end up with one or two (out of 6-9) with a green ring around the yolk. They can all be from the same carton, all cooled really, really fast or not so fast, and still one or two. I think it's just something inherent with that particular egg. FWIW, the ones that get cooked a long time in spag sauce which I mentioned in another post don't necessarily turn green, so I'm pretty sure it's not from heat.
On peeling them, I've read somewhere over the years that it has to do with the age of the eggs. IIRC, younger ones were supposed to be harder to peel, and eggs that were a little older were better for boiling. This may or may not have been from a Martha Stewart website, but it comes to mind. It may also have something to do with the diet of the chicken. All I know is that when I start peeling, if one of them sticks, usually several of them do, so I'm inclined to believe it's age of eggs or diet of the chicken.