Nice blog!
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About the ESR meter, voltage spikes on the primary of the transformer might be a problem.
Transformers are bidirectional, and this one has a ratio of 20. This implies that, if a capacitor accidentally remains charged let's say at 24V, then the transformer will generate a spike of 20 x 12V = 240V in its primary turn, at the output of the first opamp. (12V x 20 and not 24V because of the two series 10 ohms resistors, R5 and R6, in parallel with the capacitor to be tested)
It happens that long time ago I've collected a bunch of ESR schematics found online, then extracted the measuring principle from each, being interested mostly in the "input stage", or how the capacitor under test is connected to the measuring circuit. There were probably 20-30 ESR schematics in total, and the attachment is a draft of what I've scribbled back then. In fact, there were only 5 types or so in all those collected schematics:
![](https://www.eevblog.com/forum/projects/diy-analog-esr-meter-design/?action=dlattach;attach=1438594;image)
Synchronous detection will fit well in an ESR meter, indeed, as
mawyatt was saying. An example of such a schematics happens to be in the upper right corner of the attached draft scribbling, though that particular example is not directly applicable to your ESR.
To make a synchronous demodulator in principle, a multiplier will be needed, but any switch is also a multiplier with 0 or 1, so the schematic in the upper corner is using controlled switches (CMOS transmission gates from the 4066 series IIRC) to implement synchronous detection of the signal on the capacitor. In other schematics/configurations of synchronous demodulators, switches can be implemented with diodes (e.g. a diodes ring demodulator), or with transistors as well.