UPDATE (and nerd alert)
A quick update, and to let the many people that kindly contributed to this thread know their time hasn't been entirely wasted
I now have an oscilloscope and got everything working properly today. It's already opened my eyes to a few things with a lot more to come. I was recently commissioned by a photography website to test some flash guns so it'll be very useful there. Thanks to Gareth (Kaolin) for suggesting a Pico PC-based oscilloscope (high performance at affordable prices) and others that posted links to suitable photo-diode circuits. It seems there's nothing off the shelf to do this, so I built a little custom sensor and it works brilliantly. I chose a photo-diode with a spectral response very close to daylight and fast reaction time - like 1.5ns (that's 1.5 billionths of a second).
1) Elinchrom D-Lite One at full power. T.5 time is 1/2200sec, exactly as claimed, and...
2) ...at minimum power it still reads 1/1300sec. Flash durations with conventional studio heads tend to get much longer than this as power is reduced but I noticed in real-world testing that the D-Lite One was unusually fast at minimum power, and here's confirmation - it's smaller capacitors work faster (only 100Ws)
3) Yongnuo 600EX-RT in high-speed sync mode, showing how the light pulses to create effectively continuous light for the duration of the shutter cycle, giving even exposure down the frame. Total burn time is 1/112sec, firing in clusters of mini-pulses. It's not so visible here, but when you zoom in to examine the clusters, it's firing ten pulses each time, at 54,000 cycles per sec. I have never seen the very close detail of this before today. Another feature is the spikes at the beginning, that explain why the flash is actually triggered slightly before the shutter opens in HSS mode, to ensure brightness has settled to an even level right from the start.
CORRECTION: I had the sampling rate set too low, and that has created aliasing effects resulting in those little clusters of ten that don't actually exist! The flash is in fact firing at a
continuous rate of 54,000 cycles per sec throughout, at
constant brightness.
1)
2)
3) See correction in comment above