Followings are the details of the diagonalization procedure I tried in this time.

1. Horizontal sensor balancing:

To balance the horizontal sensors, I excited the lowest yaw mode (about 0.3 Hz) and measured the ratio between H1 and H2/H3 at resonant frequency.
Then, change the sensor gain ({MN,IM}_OSEMINF_{H1,H2,H3}_GAIN) so that these ratio becomes unity (this time, I set maximum absolute gain as 1).
Figure 1 shows an example of the measurement (Top 2 graphs of right column represent IM and MN horizontal sensor signal ratio from the top).
Pink and cyan line show the ratio before gain tuning, and red and blue line represent the ratio after tuning.

2. Vertical sensor balancing:

Basic concept is same as horizontal sensor balancing but used resonance is the lowest vertical mode (about 9.4 Hz).
Figure 2 show an example of the measurement.
Same as horizontal case, top 2 figure in right colomn show the ratio of IM/MN vertical photosensors.
Pink and cyan line show the ratio before gain tuning, and red and blue line represent the ratio after tuning.

Figure 3 and 4 shows the medm screen before and after tuning the sensor gain balance, respectively.

3. Sensor decoupling from horizontal to vertical DoFs:

To reduce the horizontal to vertical sensor couplings, I excited 0.3 Hz yaw resonance and measure the ratio between yaw motion and the others at resonant frequency.
What I did is check the gain and phase of yaw to the others in TF mode measurement in diaggui and set the gain at SENSALIGN matrix (If phase is 0/180, the sign of matrix element should be negative/positive, respectively).

Lower 2 rows in fig1 shows an example of the ratio between yaw and the other DoFs after decoupling.
All seems lower than 1% that would be enough at this moment.
Since L and T motions have couplings to R and P signals, I didn't decouple these two DoFs.

4. Sensor decoupling from vertical to horizontal DoFs:

Same as horizontal to vertical, I used resonance of each DoFs (V: 9.4 Hz, P: 7.5 Hz, R: 23 Hz).
Lowest 2 rows in fig2, 5, and 6 show the ratio between V/R/P to the other DoFs, respectively.
Same as horizontal to vertical decoupling, residual coupling becomes less than 1%.

Figure 7 and 8 shows the SENSALIGN matrix before and after diagonalization.

5. Health check after decoupling:

To confirm the new SENSALIGN matrix works well, I performed healt check of MN stage (results are already shown in the original post).
Since there is no large excess and some unnecessary couplings are reduced (for example, 0.3 Hz Y2R, 7.5 Hz P2L, and so on), the decoupling seems fine.

I decoupled ETMX MN photosensors more precisely.
Sensor decopling with the following method seems fine.

Detail:

Relation between measured signal vector D') and decoupled motion vector (D) can be written as follows with coupling matrix A.

So, if we can measure the coupling matrix A, we can calculate the decoupling matrix A^-1.

To measure coupling matrix, I used following resonances for the decoupling of ETMX MN photosensors.

I injected white noise around the above resonant frequency and measured the gain /phase from the excited DoF to the other DoFs at the resonant frequency (for example, TF from K1:VIS-ETMX_MN_DAMP_L_IN1_DQ to K1:VIS-ETMX_MN_DAMP_T_IN1_DQ).
Data are stored at /users/VISsvn/TypeApayload/ETMX/TF/Measurement/2024/0603/, and followings are the example of the measurement results when L resonance was excited.

Since only L has a resonance at 2.48 Hz, peaks at 2.48 Hz on the other DoF signals should be coupling.
So, coupling matrixelement can be obtained from the measurement as follows:

Here, absolute value of each element is same as the gain value and sign is same as the sign of cos({phase of coupling}) (eg. element L2T is -0.184646 in this case).
Note that, since L and T motions really make P and R motions, respectively, measured L2P and T2R couplings might not be sensor couplings, so I set zeros for those two elements.
Then, I can obtain the decoupling matrix from the inverse of coupling matrix A.

Figure 1 shows the obtained decoupling matrix, which implemented ETMX_MN_SENSALIGN matrix.
Figure 2-7 show the TFs from each DoF excitation after decoupling.
Decopling of sensors seems fine.

Note:

This time, measured T2V, P2T, P2V coupling is small enough, so I ignored them for calculating decoupling matrix (I set zeros at T2V, P2T, and P2V elements in coupling matrix).
L2T and T2L coupling becomes large after decopling matrix was implemented but it seems to be due to actuator coupling, so I will proceed actuator decopling and check what will happen after that.