If, as you say, they are "beyond saving", then no, they're useless as root-stock. They're not magically going to recover just because you graft younger material onto them.

As for scions, if these are still alive, sappy and growing healthily, there's no reason they won't grow into healthy branches/leaders when you graft them onto new healthy root-stock.

Having said that, if any of the old trees still show signs of fairly vigorous growth, I'd be tempted to try a couple of grafts onto those. Grafting is a skill gained by experiment, trial and error and the experience you gain from both failures and successes.

Don't know about root stock but we've had success by severely pruning back old, neglected apple trees back to practically just a portion of the main trunk. It rejuvenated them so to speak.

https://hortnews.extension.iastate.edu/2001/2-9-2001/prunetree.html

if the old weak trees are virus infected it wouldn't be a good idea to use them as scion sources.

I am tempted to experiment as you suggest, shaxhome, but Embothrium then gives me pause. How do I know if any of the trees are infected with viruses and whether of not they're curable? Will they infect the new Asian pears I planted nearby, or any new apple I might decide to replace one with?

Try your nearest USDA Cooperative Extension Service branch office for guidance. Due to their commercial importance Extension has done a lot of work with orchard fruits and has plenty of information about growing them. Including pest and disease issues that may be encountered.