Current transformer and amplifier + precision rectifier
I've gone down that rabbit hole a few years ago (designing precision rectifiers for current transformers). The results were unsatisfactory.

Here's a better suggestion: try to use a diode bridge directly, instead of a precision rectifier. Simply insert the diode bridge between the C+/C- terminals of the CT and the 22 Ω load, and do away with the precision rectifier. Because it's a current transformer, not a voltage source, it "compensates" for the diode drop. You could try simulating this circuit with a sinusoidal current source in place of the current transformer to see what I mean.

When I did this in my circuit, the result was cheaper and better, with no downsides, as I recall.