Is a DC servo really needed

Are you sure it doesn't just seem to settle quickly because the initial offset is already too small to do any harm? Do you notice any difference when you just ground the node R9-R10?

I had overlooked that there is also an AC coupling capacitor at the input. Maybe that's why you measure a 2 Hz rather than a 617 uHz cut-off frequency, although with the values on the schematic, I would expect a cut-off frequency just below 1 Hz.
 
Yes , without the servo ... I forgot to hook it up when I built it - was .4V.
I just let R9/10 "float' (span the +/- 11.4V) . No ground reference anywhere - simulates less than .2 (models are over optimistic).
I can't imagine why it would not settle instantly. The VCCS just does what 500R trimmers would do for the two actual CCS's.
I originally designed R14 and R21 with trimmers and had a standard servo setup. 5mV drift was typical.
Now , the servo compensates for thermals - cool.
I use it for my sub now ... actually this one (below) is 4 years old. "New Leach amp" , my favorite amp (BASS !)
We built about 20 "Slewmaster" input stages like this , they are all still moving (Very / 18") big woofers !! 🙂
OS
 

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This is (a variant of) the second circuit, the one I didn't look at in detail. Anyway:

When the offset at the output is initially 400 mV, the output of the integrator will initially change at a rate of 400 mV per second.

An offset of 400 mV at the output corresponds to 820 ohm/(820 ohm + 22 kohm) times 400 mV ~= 14.3733567 mV at the input. The tail currents will need to change by about 223.4 uA to correct for that (14.37... mV/(47 ohm + 26 mV/1.5 mA)).

The voltages across the 330 ohm feedback resistors then need to change by about 73.7 mV.

Neglecting the differential resistance of the LEDs, the currents through R8 and R11 need to change by 737 uA. The voltage at the node connecting R7, R9 and R10 then needs to change by 5.01 V.

To achieve that, the voltage at the integrator output must change about 15 V. That would take 37.5 seconds at a rate of 400 mV/s. If everything would work linearly, the rate of change of the integrator output would reduce proportionally as the offset is controlled away, so you would actually get exponential settling with a 37.5 second time constant.

I guess neglecting the differential resistance of the LEDs is too conservative, because according to this calculation, the integrator's output voltage has to go to a value it can never reach with +/- 11.4 V supplies.

In any case, I don't see how this could settle instantly.