Transimpendance and whitening are working properly. I can't get useful signal out of the differential stages yet. I replaced the channel 1 DRV134 that was burnt (very hot when powered on). But the new one got hot too after powring on, so there might be something else wrong there. I'm also wondering if it's ok to use an oscilloscope to look at the differential stage output. The scope will ground one of the two outputs: according to the DRV134 datasheet this should be ok, but I'll check better later on.
Between yesterday and today I populated one QPD board (based on D1600196), and started testing it. The transimpedance stages seems to work fine (they show about 5-6 V in ambient light). However the whitening stages show a large ~100 kHz oscillation. While trying to fix it I probably burnt one of the output drivers.