Summary:

I think the WFS head performs satisfactorily.

• The (input-referred) dark noise level at the operating frequency of 55 MHz is ~40pA/rtHz (modelled) and ~60 pA/rtHz (measured, converted to input-referred). See Attachment #1. Attachment #5 has the input referred current noise spectral densities, and a few representative shot noise levels.
• The RF transimpedance gain at the operating frequency is ~500 ohms when driving a 50 ohm load (in good agreement with LTspice model). See Attachment #2 and Attachment #3.
• The resonant gain to notch ratios are all > 30 dB, which is in line with numbers I can find for the WFS installed at the sites (and in good agreement with the LTspice model as well).
• There are a few lines visible in the noise measurement. But these are small enough not to be a show-stopper I think.

Details and remarks:

1. Attachment #4 shows a photo of the setup. 
   • The QPD used was S/N #84.
   • The heat sinks have a bunch of washers because the screw holes were not tappe at time of manufacture.
   • There isn't space to have 8 SMA feedthroughs in the D-shaped cutouts, so we can only have the 4 "RF HI" outputs without some major metalwork.
   • C9 has been remvoed in all channels (to isolate the "TEST INPUT").
2. I found that some quadrants displayed a ~35 MHz sine-wave of a few mV pk-pk when I had the back of the enclosure off (for tuning the notches). The hypothesis is that this was due to some kind of stray capacitance effect. Anyways, once I closed everything up, for the noise measurement, this peak was no longer visible. With an HP8447A preamp, I measured an RMS voltage of ~2mV rms on an oscilloscope. After undoing the 20 dB gain of the amplifier, each quadrant has an output voltage noise of ~200 uVrms (as returned by the "measure" utility on the scope, I don't know the specifics of how it computes this). Point is, there wasn't any clear sine-wave oscillations like I saw on two channels when the lid was off. 
3. Some of the lines are present during some measurement times but not others (e.g. Q4 blue vs red curve in Attachment #1). I was doing this work in the elec-bench area of the lab, right next to the network switches etc so not exactly the quietest environment. But anyway, I don't see anything in these measurements that suggest something is seriously wrong.
4. In the transfer function measurements, above 150 MHz, there are all sorts of features. But I think this is a measurement artefact (stray cable capacitance etc) and not anything real in the RF signal path. Koji saw similar effects I believe, and I didn't delve further into it.
5. The dark noise of the circuit is such that to be shot noise limited, each quadrant needs 10 mA of DC photocurrent. The light bulb we have has a max current rating of 0.25A, with which I could only get 3 mA DC per quadrant. So the 55 MHz sideband power needed to be shot noise limited is ~50 mW - we will never have such high power. But I think to have better performance will need a major re-work of the circuit design (finite Qs of inductors, capacitors etc).
6. Regarding the transimpedance gains - in my earlier plots, I omitted the 50ohm input impedance of the AG4395A network analyzer. The numbers I report here are ~half of those earlier in this thread for this reason. In any case, I think this number is what is important, since the ADT-1-1 on the demod board RF input has an input impedance of 50ohm. 
7. Regarding grounding - the RF ground on the head is actually isolated from the case pretty well. Two locations of concern are (i) the heat sinks for the voltage regulator ICs and (ii) the DB15 connector shield. I've placed electrically insulating (but thermally conducting) pads from TO220 mounting kits between both sets of objects and the case. However, for the Dsub connector, the shape of the pad doesn't quite fit all the way round the connector. So if I over-tighten the 4-40 mounting bolts, at some point, the case gets shorted to the RF ground, presumably because the connector deforms slightly and touches the case in a spot where I don't have the isolating pad installed. I think I've realized a tightness that is mechanically satisfying but electrically isolating.
8. I will do the fitting at my leisure but the eye-fit is already suggesting that things are okay I think.

If the RF experts see some red flags / think there are more tests that need to be performed, please let me know. Big thanks to Chub for patiently supporting this build effort, I'm pleasantly surprised it worked.