Okay, so after developing another version of the cooling add-on (that's far more mechanically robust and requires no printing supports), I have finally managed to keep the thing cool.

And by cool I mean stupidly cool - We're talking only a 5-10 degrees Celsius rise above the ambient.
It turns out it needed minimal air flow (of any amount) to move the little amount of heat it's producing.

Here we go:

It's not the prettiest looking case accessory, but it certainly gets the job done via the 1W/5V USB fan. Now instead of going from 23C to 75C in 2 hours it goes from 23C to 30C in 20 minutes.

I also had a look at the waveform directly to see if the fan attachment was coupling any EMI to the measurement circuit. Turns out it isn't! I also tuned the output filtering pF capacitor a little to ensure that the RF/op-amp oscillation fluff was minimised.

Next step is the MATLAB stuff!