What is the best method to compensating offset at the output of a peak detector circuit?
According to my  calculations, there is a gain in this amplifier of almost 3800. Your 4.7mV offset implies &lt; 2uV of input offset voltage, which is really very good for any amplifier.

Instrumentation amplifiers can have offset voltages lower than this under ideal conditions but across temperature they will not be quite as good.

My question would be, why do you want to null this tiny offset when it refers to a tiny input offset?

See my comment that R11 and R13 should be the same; this is quite likely the cause of offset in the simulation (I may run it later when I have some time)

If you really need to offset this output, then I would use a precision reference and a follower into the final output amplifier.

Note that the tolerance build-up of your components in a real application will very probably dwarf this offset you have.

To overcome this, you may wish to use a precision instrumentation amplifier.

HTH