Thanks chaps. A clear gap in my knowledge here so I spent last night reading up on the workings of stator windings and reg-recs. As you say, any fault in the stator is most likely to lead to loss of voltage rather than a spike.
It was the fact that my last reg-rec was definitely overcharging and the new one seemed to be going the same way that led me to think something else was amiss further down the line.
Anyway, it all checked out today. Output voltage is still good. When the bike voltmeter was off the scale at high revs my multimeter on the battery was still happy.
I attached the multimeter to the bike's voltmeter terminals and tested again. Same result - voltmeter going daft but multimeter was showing normal voltage. The voltmeter I fitted is clearly haunted, probably by the ghost of Michael Faraday who is angered by my lack of electrical understanding.
It turns out the only problem on the bike is the thing that I fitted to warn me of problems on the bike.
I switched my multimeter to "irony" and got a very high reading.
