Guidance wanted - measuring nanoamps reliably (with Dave's microcurrent)

[Puffin]

I'm working on a long-lifetime coin-cell powered design with a draw of 200-700nA and trying to measure the load using an EEVBlog microcurrent gold, but what I'm seeing is that the readings are varying quite a bit [+/- 100nA] just depending on how close to the bench I'm sat, and by up to -500nA if I put a hand near the DUT.   My test leads to the microcurrent are short, but I've just got standard meter probes on the terminals leading to the meter -- using a Fluke 175  [Side note - I initially used the EEVBlog BM235 but it shows drops of 100-400mV if I move anywhere near the test leads!  The Fluke doesn't twitch more than 20mV]

I can take my readings at a distance, and thus get myself out of causing the influence, but the whole setup seems more sensitive to external influence than I expected in general anyway and I'd like to be sure the readings I'm seeing are actually sane [They're actually about 2x what I was expecting, but that may be correct...]

So I'd appreciate suggestions for best practices for measuring such low currents and use of a microcurrent gold, especially down at nanoamp levels.   I'm very much a noob at caring about these sort of low currents.

TIA

[timpattinson]

Sounds like an EMI problem... Have you tried putting the whole thing in a big tin can? (~= Faraday cage)
Turn off any fluorescent or LED lights?  Turning your phone  (in your pocket presumably) off?