[meteoestarreja]

For your lab test to mimic my conditions you would need to apply a constantly shifting voltage to the input, varying say 2v up and down in less than 1 second cycles.

I never imagined that the speed (frequency) was that high!
In deed, the fastest frequency that I used was around 1 to 1,5 Hz, but you said that in your case is faster than that.
The more strange to me is the fact you're using a battery/solar panel, so, it shouldn't be anything to do with ripple or something like that (even that the regulator itself tends to filter the ripple, and if you are using capacitors, definitely ripple shouldn't be the "killer" here).
I will try to reproduce later if I can find anything at home that allows to run at the same conditions ... I'm leaving the office

Just for curiosity, how did you managed to read both high and lower peak at that frequency?
You used a oscilloscope or your voltmeter do record high an low values?