Gary,

I don't know a lot about grafted plants, but since you're trying to do this when the ambient temps are generally lower, I would suggest to you that you get a heating mat, in order to provide bottom heat to the degrafted scions. What you state sounds reasonable to me, but I'd make that layer of soil thin and give the rooting scions (especially if you have the aforementioned bottom heating in place) a mist or two every several days.

I find it interesting that your stocks are dying - I wonder why, as do you, I'm sure.

I think you need to let them dry for more than a few days, I am more used to weeks to months. The rest is correct, except that i don't understand what you mean with "button". Also, as the Astrophytum scions are so much bigger than the Pereskiopsis stocks I cannot see why these "buttons" would be 1/2 of each.

Gary,

If you can post some pics of these 'buttons', at least two of us will have our curiosity answered. Now that TJ mentions it, it wouldn't hurt them to dry for at least a week. While they're still wet from the slicing and dicing (wait, no dicing) I'd put one of those rooting hormones on the cut end of the scion (but that's just me - perhaps they will just as easily not need this to root).

Thanks 'cactusmcharris' and 'tjicken' I appreciate your responses. I've tried to take pix of the mysterious "button" I mention...but my camera refuses to micro focus. To explain further-where the scion and stock meet a small thicked round growth is present. This is what I am calling the button. It is the actually spot where the graft occurs and is much bigger than the persik. and much smaller than the astro. The scion and stock have formed an 1/8th inch thick round 'growth'. My comment earlier was that I perceive this rounded thick area to be 50% scion and 50% stock. I was wondering whether to de-graft(slice) 1)above the button, 2) thru the center of the button, or 3) below the button. I hope this is a little clearer explanation for you. Thanks again, Gary

Ah, I understand, it's like a scar, I would think you would want to cut just above it or slice it off. That way you get rid of any possible graft material and any damaged tissue from the original graft.
Tally HO!

The scion often grows slightly downwards, forming a cap around the top of the stock, I guess this is your "button".
If the Pereskiopis is dead I would try to remove those parts completely, i.e. cut just above the button. Actually I would do that even if the stock was alive. I have heard that remaining parts of the stock is not harmful, and that such remains die when the scion grows roots of its own, but I cannot confirm that, and I prefer to know what kind of roots my plants have.