I think the precision due to the loop gain uncertainty is something like 0.1% at 0.1 Hz. It's not the issue.
The real issue was the loud motion of MICH, which degrades the coherence of the measurement.
Also last night I tried the fringe hopping technique and gave it up for several reasons.
(uncertainty due to the loop gain)
(Effect from the MICH motion)
This seems like an error prone method for DC responses due to the loop gain uncertainty. Better may be to use the fringe hopping method (c.f. Luca Matone) or the fringe counting method