I'm quite interested in this subject. The paper I've read the most is another one from Julian Parker.
I suggest that you try recording the spring output when you put in a "click", that is, a very narrow rectangular impulse.
Record that into Audacity and then select spectrogram (-graph?) view.
I think what you are measuring is the overall time delay going down the spring. Notice that you are getting a distortion of the waveform apparently... it no longer looks like a single sine cycle. The second half has a higher peak and I believe that this is the dispersion effect in action. A single cycle of sine wave is closer to an impulse than a continuous sine wave, spectrum wise (IMHO).
Since the point of multiple springs is to reduce the boing by spreading things out a bit, if possible disconnect one of them and just focus on that.
Thanks for the reply!
I've read the Parker paper as well.
About the 'click', I will try but I thought a single period of a sine wave is as short as it gets to test a single frequency.
Yes, I'm getting distortion but I think this is mostly due to my very crude testing equipment.
My signal generator is my laptop headphones output recorded into a Ditto looper pedal.
For whatever reason, it will not record or output a symmetrical sine wave.
The looper directly connected back to my USB interface (not going through the reverb) shows that top and bottom of the sine wave do not have equal amplitude, which then obviously also shows up in the reverb output.
The 'example' input I showed in the previous post was when it was still in my DAW. Once recorded into my looper pedal the top amplitude is greater than the bottom peak amplitude.
Another hindrance is that the Surfy Bear does not have a flat frequency response for the reverb output. It severely attenuates the lows. I guess some of the filter effects show up in the recorded wave output when testing lower frequencies.
None of this has any effect on the measured delay time though...
About using a spectogram instead. I tried that as well and I will get the same results as I'm seeing in the spectograms in those papers.
However, to me it seems the spectogram view shows the repeat as a whole and because it 'rings' out longer at higher frequencies there's more energy later on as well than purely at the onset of the repeat which is why it looks like higher frequencies arrive later.
Consider the 4000hz repeat below.
It clearly starts at 31ms but only the first period of the repeat is 4000hz, the following periods are shorter and shorter, showing an increase in frequency (although the input was a single 4000hz sine wave).
It 'rings' out so long that it overlaps with the first repeat of the other spring which arrives 8ms later.
I'm thinking that the spectogram view shows this as 1 repeat and one way or another calculates the amount of energy in that longer time and this is what is causing the seemingly delay for higher frequencies.

I don't know (yet) if the 'trail' of the repeat is caused by the input, introduced along the way in the spring or if it's simply the lasting vibration of the output magnet.
At the moment I'm thinking it's similar to how a spinning coin ends. It has a similar ever increasing frequency towards the end:
The point of multiple springs, I thought, was to prevent hearing the repeats of the spring reverb as individual repeats. The more springs (of different length) the smaller the interval between individual repeats, giving a more dense, smooth realistic reverberation effect. It's not going to affect the delay of the other springs.
But I'll try it later on today with the other spring dampened. Even if it were just to see how long one repeat rings out.