After continuing to ponder why the analog circuit was not functioning, I decided to play with it a bit more. I found one wrong connection and added a schmitt trigger input to the reset comparator.
The results are encouraging. Obviously it needs some refinement. But this curve set is unmistakable as that of a NPN. The ugly drooping of the collector-emitter bias is likely due to the high output impedance and poor voltage regulation of the passive supply. A voltage follower might solve this issue.
I also redesigned the part that supplies collector current, and thought about how to use it for PNP devices, though my first idea is wrong. The schematic below reflects these changes, including the wrong idea.
After more fiddling around, and some more circuit changes I started to get nicer plots like this:
It looks like I have base bias stability problem. More tinkering on this is sure to come.
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