Hi. Thanks for the comments.
I take the points about the layout. I accept I was being a little bit creative in my interpretation, and I perhaps chose a somewhat inappropriate project for my 2nd ever PCB.
I'll confess I struggled to understand what was going on in the single regulator demo board (although having revisited it, I suspect I was being confused by the lack of labelling of the traces to the measurement ports). So, I took a bit of a gamble leaving out the magnetic field cancellation, and also as it had been left out of a number of boards I'd seen for sale (not necessarily a good sign, I concede), and a successful board design posted elsewhere on this forum. (
https://www.eevblog.com/forum/chat/why-did-my-lt3042-die/). Instead, I added some electrolytic caps to avoid the ceramic cap resonance problem.
In terms of the external NPN transistor, this has almost no effect on noise whatsoever. Both LT claim this in a technical note (
https://www.analog.com/en/technical-articles/increasing-output-current-of-the-ultralow-noise-ultrahigh-psrr-lt3042-200ma-linear-regulator.html) and measurements on the other thread report this. There is an impact on PSRR, but I wasn't really aiming for that.
After some experiments, I think the problem is as Vovk_Z says: common mode noise compromising the measurements.
I made whatever changes I could to the board (rearranged the Kelvin connnections to R4/C5 and C14), added an ceramic cap to the twisted input wires (as a crude magnetic-field cancelled decoupler) but these did nothing measurable.
Then by accident I shorted the probe (tip and ground) to a ground pad on the board, and was surprised to still see the spikes unchanged on the scope. At this point, it became clear that this had to be a common mode problem.
I also tested the regulator with a battery, and when completely isolated, the regulator gave a clean output. However, if one side of the battery was connected to one side of the bench supply, the spikes came back at identical amplitude.