I think I had underestimated the responsivity of the Silicon PD at 1064nm. The previous value was based on a rough search online for the responsivity of Silicon (I couldn't find the product number of the actual PD we are using). For instance, the PDA100A Si detector from Thorlabs has a responsivity of 0.35-0.4A/W at 1064nm.
If we calculate the responsivity of the Hartmut PD from the measurements I made today (input power = 0.300mW, output voltage = 5.56mV, effective transimpedance = 80 Ohms), then the responsivity at 1064nm is 0.23 A/W which is not an unreasonable number given the response of the Thorlabs detector.
There is one other troubling point: using the estimate of responsivity on the Harmut PD * incident power * transimpedance at DC = (0.02A/W) * (0.28mW) * (80 V/A) = 0.45 mV.
But the measured DC voltage is 6.5mV = inconsistent.