After painful trial and error process we've found a solution that converges.
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Demod phase and sensing matrix changed again. Rephasing and one DOF worked but not others.
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In the end we ditched the angle dither because it was very unreliable, and instead used length dither (see Stefan's alog).
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I stopped trying to obtain a nice input matrix that gives me hard and soft, instead started doing WFSA and WFSB based feedback because it's simpler. The output matrix still goes to hard and soft, and it worked.
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After phasing and manual alignment and centering, engaged the servo one by one, centered WFSs. After some trial and errors and numerous freezeing workstations, we got something that converges.
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Linear range of the things is very narrow. Give things somewhat large offset and the servo ran away. Off-centering of 0.1 or so makes things much worse.
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Right now the bandwidth of things is small, probably UGF is smaller than 0.1Hz.
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We started trying to diagonalize the system, but after N reboots I had enough.