Stool Bed Propagation of Grafted Trees

I'm thinking through how to propegate grafted select varieties of trees. Grafting is cool, but it doesn't bring new trees into the world, just put one trees' genetics on top of another trees roots. So how can I take a select variety of tree and actually multiply it.

I'm thinking about creating a stool bed with a grafted tree. Specifically paw paw. What if I took a grafted paw paw tree, laid it down on top of the soil, mounded soil around it's roots (so the tree is planted horizontally). Then as it sends shoots up (from the graft) in the spring mound sawdust around those shoots. I'm imagining this would great a productive stool bed where I can dig up the shoots in the fall and they will each have their own root. So I would have created a handful of new paw paw trees that are select varieties but on their own root systems.

Any thoughts? Anyone try something like this?
I've attached a screenshot from Akiva Silver's book to highlight what I'm thinking. He suggested doing something like this as a way of propagating root stock. But Im wondering if it can be done to propegate the graft.

The only thing I feel like is worth paying attention to is making sure the rootstock doesn't send up shoots. I wouldn't want those shoots to mix in with the select variety shoots.

I've done that with differing apple rootstock. Works well. 5 small sized trees come off that per season per horizontal tree. After three years.
I keep the cutoffs potted up for a year after, in half shade, to get them taller than grasses and get them to make a more robust root system before planting them in winter.

Ok great! This is encouraging. Any problems keeping the rootstock from sprouting or getting mixed up with the graft? And I guess after I've gotten a few grafts to root I could create a horizontal bed with those and have no root stock to worry about.

My goal was to get good rootstock on the go, one that does well where I live and graft onto them later when they were on their own roots. Bittenfelder for me medium height and high I chose.
But only this year I managed to master grafting somewhat.
So some are man high already. What gives? Enough place with the government turning against farmers and the older generation retiring and hardly no young farmers..
The second part of your question confuses me slightly. I take it you mean cutting instead of graft. You could do that. But the thing is the whole grafting thing is based around rootstock, which is a tree with a strong healthy root system but not very appealing apples and grafts. Grafts are the opposite, have great fruit but a weakish rootsystem with weak growth.
Although some people got grafts on the go and say it worked fine.
Isn't pawpaw grown from seed most often? Then it doesn't matter.
If you got time and space the Akiva Silver method is totally worth it. Man deserves a statue.

I have had rootstock sprout along the whole length during storage.  Haven't tried Paw Paws, too cold, here but choke cherries work well if I layer an entire branch I get multiples.