Hi Karen,
I also grow Ashmead's. A lovely apple! Sorry for this delayed response, I have been traveling over the last month, but I wanted to chime in.
Apple Mosaic Virus is the result of infected plant material being moved around by grafting or even by plant to plant contact (such as underground root grafting, one tree to another, that can take place over time)
Some varieties show it much more than others. Plus, it is known that Apple Mosaic Virus can spread to many other desirable fruit species too (including plum, peach, pear, cherry, blackberry, roses and more)
To the best of my knowledge there is no cure for Apple Mosaic Virus and though the trees could limp along (and technically survive) they will have reduced vigor, reduced fruit production and they are a source of infection to all your other adjacent apple trees and in my opinion the trees should be removed.
I would not plant any other apple trees in that spot, for a season or two . . . Cover crop the area, and soil build your biology, then be sure to source disease free trees from reputable focused sources only. . . Cummins, Fedco, Trees of Antiquity, Dave Wilson, Salt Spring Apple Co., etc. . . Van Well Nursery in Washington is a solid source, but they do not offer Ashmead's and are more focused on mainstream varieties, but they would be well worth contacting.
Losing the 4 years you have with those trees is tough, all the care and attention, and time lost in their establishment, training and development . . . As a fellow apple farmer, it is sad to me too, and I truly empathize.
Lets us know what you decide to do . . . and feel free to post up pictures of your virus for those less familiar with it too. We can all learn from one another, no doubt about it.
Love that you are going big on the cider variety front. Wishing you loads of success!
Cheers!
Gopher Hill ApplesZone 8 in California