I have put an offset of 1000 counts to C1:SUS-ETMX_ALS_OFFSET. This actually misalign the mirror a lot.

While the offset is applied. I adjusted the balance of the coil matrix.
UL 1.580 UR 0.620
LL 0.420 LR 1.380

> ezcaread C1:SUS-ETMX_TO_COIL_0_0_GAIN
C1:SUS-ETMX_TO_COIL_0_0_GAIN = 1.58
> ezcaread C1:SUS-ETMX_TO_COIL_0_1_GAIN
C1:SUS-ETMX_TO_COIL_0_1_GAIN = 0.62
> ezcaread C1:SUS-ETMX_TO_COIL_0_2_GAIN
C1:SUS-ETMX_TO_COIL_0_2_GAIN = 0.42
> ezcaread C1:SUS-ETMX_TO_COIL_0_3_GAIN
C1:SUS-ETMX_TO_COIL_0_3_GAIN = 1.38

Now, we can keep TEM00 for green with +/-1000counts of push although the fast step of the offset make the lock lost.

It turned out that the step longitudinal input temporary misalign the mirror in pitch because the length and pitch are coupled.
I guess that we don't excite pitch if we push the mirror slowly. Eventually, we need f2p transfer function adjusted in the output matrix.