OK, I built this. I know there were a good few changes suggested, but I was relatively confident it would work (perhaps with a couple tweaks) and really wanted to get on with it...
It seems to work quite well. More testing will follow (and I've only posted screenshots of the low frequency output, though the high frequency one works just as well).
Couple things -
- I of course missed the input bias current of the instrumentation amp, which at 250nA on 470k and a gain of 200 would have the thing shooting for 24V... so I removed the 33k differential lowpass resistor and changed both 470k bias resistors to 33k.
- Added a switch to DC-null the inputs. Not really necessary, but it does stop the amplifier from saturating after power is applied, which allowed me to actually watch the settling time.
- RC time constant of the first input coupling stage is 1034 seconds, and 73 seconds for the second stage. Yes, this takes a
long time to settle (plot attached).
- No need for batteries. The noise floor is indiscernible even powered externally.
- Clearly, from the layout of the panel parts (jacks and battery clips) I didn't plan the housing very well

Pictures:
- Inside the box. Yes, I built it in an electrical junction box. Works nicely.
- Closeup of the circuitry.
- LF noise floor with both inputs terminated.
- Output noise of my Power Designs TP343A.
- Settling time.

- Schematic.
The only thing I think I'd change if I redesigned it would be to add an offset nulling control to the LF output, so I don't have to use the oscilloscope to do it.