No, I haven't tried reinstalling everything, because further Googling indicated it's an inherent problem with the latest version of Chrome, so reinstalling is unlikely to have any effect (I'd still be installing the same bug).
The date problem is also not unique to me, and seems to be a Chrome thing too. So I guess I've just got to wait for one or both to be fixed in the next release.
I've found several accounts of both problems, but no reports of a successful fix to BOTH. Many people have done what Tony (NOT Cheshire Man

) recommends, and which I've already tried, which is to revert to a manual install.
Yes, that did work for me, up to a point - i.e. it installed - which was an advance. But now I have Problem 2, which is that Chrome insists the brand new installation is already out of date. So I can now run Java, but only after dismissing the warning every time.
The only way to stop it would be to disable warnings for ALL out-of-date plugins, which I don't want to do, because presumably some of them might actually be genuine.