@Jeffro - Sorry, I'd gone to bed.

I expected to see it this morning, but no. "Check Again". "You have the latest, 3.6".

My WAMP server is old. I did not delay, to check the vitals. But all else works; plugins are updating ... and this has been my bargaining-line: Any hickup from WP, and we have to rebuild, regardless.

This setup has updated/performed flawlessly, for a 'long time', but it is getting old. Yes, it will be a big hassle; I want to move to a different arrangement, rather than perpetuate this one, at high cost. It won't be hard to get the server-specs....