Hi guys, thanks for the suggestions. I don't have immediate access to a scope, though I think I could borrow one. Here's the 'progress' on this:
After rummaging about under the encoder's casing, and concluding that I was way out of my depth, and it was fixed to the servo in a way that was NOT letting me take it off without damage, I put it all back together as best I could and... The problem has disappeared! Leaving me both pleased and with the sense that it will probably come back when least convenient. For now though it's been working for some time without any signs of missing a beat.
A tentative hypothesis is that maybe there was a speck of dust or other build-up on the scales that got dislodged, or probably more likely, there is some loose connection that got pushed about and is slowly working its way loose again...
At this point, as I have tested the servo with a known working drive and cable and it was still playing up (back when it was playing up), I think I'll just order another second-hand servo as a spare ready for if/when any of the four fail.
Thanks again for your input guys.