As expected, the verdict is that I need a new prescription, both for near- and -far vision. The good news is that I finally get to abandon bifocals (or 'progressive lenses' as they're called now), which I've always hated and have had to put up with for forty-seven years. Instead I'm getting two separate pairs: one for short-range (reading a book, working at the laptop) and the other for everything else (also known as not-running-into-things). But instead of one main 'progressive' set and one non-progressive reading set I'll now have one for near and the other for far, pure and simple.
The unexpected news was that the reason I've been having problems with the ranged vision, such as it is, is that my long-range vision has slightly improved, so that my old glasses no longer quite match what I need. That's never happened before. I always assumed my eyes would keep getting worse and worse, since this is the experience I've had ever since I started wearing glasses in third grade (and had confirmed every time I've visited an eye doctor from the age of ten onwards). Imagine my surprise when they'd told me last visit that they thought my eyes would stabilize over the next decade or so and then actually begin to improve somewhat. That prediction now looks to have been on the mark: my new long-distance/general duty glasses will actually have a slightly weaker prescription than my current pair. Weird. But welcome. Even so, it'll take longer for my distance-vision pair of replacement glasses to arrive: they have to send off for the lenses.
And yes, I still have elongated eyes (apparently a side-effect of the near-sightedness). Which gives me a bit of sympathy for Smeagol and his 'long eyes'.
And now, to await the arrival of the two new pairs of glasses!