Thanks to DougM for his suggestions! The problem is now fixed and we are on the road again.
The alternator windings were burnt out even though the resistance measured correctly. Measuring the alternator output with the rectifyer/regulator connected misled me when comparing to the other bike. It has to be disconnected to get meaningful readings - I don't know why! Anyway, when I removed the windings the damage was obvious.
I replaced both the alternator and the rectifyer/regulator, as a failing RR is often the cause of a burnt out alternator. It can sometimes run fine for hours before it starts misbehaving. I didn't want to risk destroying my new windings.
Strangely the bike was unable to charge the flat battery during a 60km run, but a workshop successfully charged it. It took 3 hours before it started accepting the charge. I am now keeping a close eye on it just in case it dies!
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