If you are not wanting the original roots to sprout, you could just leave it as-is until next spring.
Otherwise, you could do it anytime before it gets to be too cold there.
Most elms respond well to hard cut back and/or defoliation. Since you've already got roots, you really don't need foliage for a while, so you could hedge-prune and probably even fully defoliate it so you won't have desiccation issues, but I seriously doubt you would anyway. So probably all you need to do is shorten branches to facilitate your digging, sawing and potting of your ground layered tree and also the old roots --> you may get an interesting bonus. Keep the ground layered part in the same location or light conditions as where it is now. If that isn't full sun, then subsequently introduce it to full-sun over the course of several weeks so you won't have 'sun-burn' leaf issues.