The problem turned out to be with the target camera. Despite getting pretty bang up results with the PSD's and modal sequences, there was basically no difference between the average intensity profile with the classical or LTI controller. I spent several days trying to find some intensity-based performance metric-power in the box, image sharpness, intensity variance-that would show some difference to no avail. Eventually I just gave up and averaged a few thousand HDR frames and found both controllers yielded essentially identical results; no function of profiles was going to reveal any advantage.
Why this happened is still a mystery considering the improvement in the PSD's with the LTI controller. I suspect its because there's enough power in the uncontrolled 26 modes to swamp any gains. Looking at the modal distribution of the open-loop disturbance wavefronts confirms that there's significant power at the higher spatial frequencies, and indeed both the classical and LTI controllers knock down roughly similar amounts. Luckily both almost completely eliminate the steady-state (average) disturbance in the controlled modes, so at least something is working.
Note that since the modes are not unitary, you can't compare the norm of the time series of the individual modal sequences directly. Instead, you have to multiply each one by the spatial norm of the mode's phase shape (sort of like the spatial RMS), to really get a number that's proportional to the "power" produced by that mode.
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