You said 3:50, I see that as posted at 4:50. I assume it is the local time that is shown.
I can't see any reason to match capacitances. That is purely parasitic and in parallel with the tuning cap which is adjusted for resonance which takes the parasitics into account.
Anything that lowers Q I would not want to duplicate, but a bit more or less stray capacitance won't hurt either way.
I know, but I am suggesting the Boonton can be replaced, likely as easily as improved.
I'm not sure it's that simple. Zeroing the meter in this circuit is not the same thing as compensating for the diode drop. I believe you zero the meter with no input signal, no? The zero adjust would need to be adjusted for zero, but you won't see a negative, so it will be a bit tricky. You can't tune it up and down past zero, it will only go to zero and stop no matter how much more you adjust it. I guess it can be done.
I would just scrap all the electronics in the Boonton really. This circuit is from a time when the active elements would be minimized (unlike today when we throw transistors at a problem to make it work better). You don't need 283 volt power supplies for your FET. Why keep all that instead of just using your K-amp and building a pretty simple active diode circuit? Then the meter will not even need a zero adjustment and in fact, you won't need a dial meter. You can use a very simple ADC and digital display, like a standard voltmeter. In fact, with an AC voltmeter you don't even need the diode circuit. Measure the AC value directly and calculate the Q from the input value.
I think if I were doing this I would salvage the thermocouple so the input can be measured. I would use something like the K-amp to provide a 1:1 copy of the coil voltage. The output of the thermocouple and K-amp could be measured with the ADC of an MCU approaching 12 bits of accuracy, or a standard voltmeter can be used to make the measurements. Some very simple calculations and there's your Q number.
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Is that mV or mA? Meters actually work on the current and are usually specified with a current and the coil resistance although the voltage and resistance gives you the same info. I believe somewhere you said the meter was 1.2 kohms. Yeah, in the "simplified" image you said the meter was 100 uA and 1200 ohms. Is it actually 100 uA and 1600 ohms which would give 160 mV?