After a few days of topping off the rear tire on Mary’s bike, with no gashes or debris in the tire, I finally replaced the Michelin Protek tube and autopsied it:
While it’s possible to extract the valve and perhaps even clean / replace it, I think that’s just delaying the inevitable. The rubber shreds may be necessary to fill large punctures, but they seem to wreck the valve seal.
Her bike now has an ordinary (pronounced “cheap”) tube inside the Schwalbe Marathon Plus armored tire. We’ll see how long this lasts.