Then you might consider just averaging many samples using an RC passive filter as in the post #13 circuit, with a higher corner frequency so it settles in a shorter time.

For example an RC time-constant of 50ms will settle to within 99.3% of the final value in 500ms, so then you average the last 500ms to reduce the ripple and get a low-noise value.

I just might try that and see what kind of readings it gets. I simulated your circuit from post #18 on my end, and I'm curious where did all those component values come from? I tried substituting some resistors with more common values, and and it seems like it hasn't noticeable affected the output.

Ideally, instead of taking samples for 1 second from each of 10 current clamps within a 10 second period, if I could, I would sample each of clamps more rapidly, and have more of an "average" value over the last 10 seconds for each of the 10 clamps. With an active filter, I probably would be able to do better than a higher corner passive?

U2 seems superfluous in that circuit? In the sense that I can do multiplication by 1.11 in software. If so, I probably could get away with one DIP8 op-amp, doing the work for U1 and U5.

What's the signal frequency?
Can you precisely control the A/D sample frequency?

The frequency is mains 60hz. I can control sampling frequency, but not in a precise way.

What I'm still trying to wrap my mind around is how this circuit will treat non-standard sine waves coming out of the current clamp, and how different averaging methods mentioned above tie into that. Some of my loads would be far from PF = 1.

 

where did all those component values come from?

They are somewhat arbitrary, but the input and feedback resistors should be the same 1% value so that the plus and minus parts of the waveform have gains within 2% of each other.
R4 and R5 determine the gain, of course.

I probably would be able to do better than a higher corner passive?

Possibly.
May need to determine that by trial and error.

U2 seems superfluous in that circuit?

It superfluous only if the load is very high impedance (1 megohm) and there is no passive filter on the output, since the U1 circuit output impedance is 40kΩ for the positive portion of the input waveform (U1 output is 0V).

What I'm still trying to wrap my mind around is how this circuit will treat non-standard sine waves coming out of the current clamp, and how different averaging methods mentioned above tie into that. Some of my loads would be far from PF = 1.

It depends upon the amount of distortion in the input waveform.
For best accuracy you could calculate the RMS value of the samples (average of the square-root of the sum of their squared values) to get the true RMS value of the current (with no analog filtering, of course).