Summary:
The problem of "Sense" pin of OMCA QPD1 short-circuited to the BHDS structure (alog 90029 from yesterday) was tracked down to the free "sense" wire inside the QPD enclosure touching the aluminum part inside the enclosure. We solved the problem by trimming the wire short.
Merely opening the QPD enclosure broke the short circuit temporarily:
We lifted the OMCA QPD1 from the BHDS while QPD2 is still attached to the BHDS and confirmed that the sense pin for the QPD1 is conductive to the QPD1 enclosure but not to the BHDS. As soon as we opened the back of the QPD1 enclosure, the short-circuit to the enclosure was broken.
It seemed that the free part of the sense wire was a bit too long and bowed in the enclosure, allowing the tip of that wire to touch the inside wall of the enclosure itself (see Elenna's first image in her comments).
Cutting the sense wire short broke the short circuit permanently:
I cut the wire short such that it cannot touch the enclosure (Elenna's second picture), reassembled the enclosure and confirmed that there's no short circuit between the sense pin and anything else.
Repeating the tests:
We put the QPD1 back on the BHDS and connected the cable to the transimpedance amplifier. On the oscilloscope, it was immediately apparent that the terrible 60Hz noise (which was 6.5V p-p) was gone (Elenna's 3rd picture).
We repeated the flashlight test, all segments responded with O(1)mV negative voltage (i.e. positive output minus negative output from the TIA amplifier was negative few mV maximum) while the dark offset was O(0.1mV).
We also measured the dark noise. It seems that all measurements for both QPD1 and QPD2 were limited by the noise of the TIA. Low frequency noise especially 60Hz and its harmonics varied from channel to channel, but in all cases it seemed that there's very little difference between the noise measured with QPD connected VS the noise without QPD. As such, I'll just show here a few examples. First attachment is the QPD1 segment 1 noise with the QPD attached, the second is the same thing but without QPD connected to the front panel of the TIA. They look identical. The third one is the QPD1 segment 4 (with QPD attached, not much different without QPD). The fourth one is the QPD2 segment 3 (with QPD attached, not much different without QPD).
There's no reason to suspect that QPD1 for OMCA is broken (nor QPD2).
Here are photos of the QPD housing with the back removed. You can see a long unsoldered wire that we identified as the "sense" wire with conducitivity tests. This is pointed out with the pink arrow. You can also see an extra mystery wire pointed out by the blue arrow. We don't know what that wire is attached to. The wire pointed by the blue arrow is actually the shielding wire which is connected to pin 1.
The after photo shows the sense wire after Keita clipped it short, pointed out with a pink arrow.
I have also included a photo of the oscilloscope image of segment 1 of both OMCA QPDs.