Can you start a layering now in late summer and leave it until the following late summer or fall? What if you are layering branches in the ground near the original plant so it was a chancy it didn't freeze.
DhD
Not sure what was not clear about:
"All layers are started in spring, around the time the foliage has expanded and started to harden off"
But:
End of summer, so almost autumn, leaves falling, less and eventually no transport of nutrients (or rather: hormones) to the air layer, no forming of roots, so I'd say: no, that's probably not a good idea.