I would identify what end result I want for the textile - to stabilize for conservation, to restore to use or a combo of conservation and restoration - meaning you don't intend to use the item but want it looking as near to the original as possible. That will determine what to do.
On any restoration job there is The Ship of Theseus paradox or known here in the UK as "Trigger's Broom"
If you want the combo and accepting that this would not be considered an important historic textile....
Decided on your pattern first. Leave the textile in one piece as long as possible (for all three scenarios)
As you stated the back is too far gone, I would embroider through the old backing. The old backing is providing support for the existing embroidery.
Then I would layer the whole quilt onto a new backing with the old one still in place. Keeping as much of the original textile as possible. That old backing is still part of the textile's history.
As for quilting, you could either re-quilt along the same lines, removing the old stitches as you go or perhaps quilting a minimal but complimentary pattern whilst keeping the original stitching in place. Does it matter that the front and back quilting isn't the same?
If you could do it on a slate frame all the better, but they do take up room. If you want to go that route, anybody that is handy in the woodworking dept can make you one with some long bits of wood and some upholstery webbing stapled onto it. You support the frame on some cheap trestles from IKEA. A square hand quilt frame is nearly the same thing but costs a whole lot more
HettyB