I've applied the technique suggested by Knox-Thompson to all
frames of a movie, and calculated the average phase.  The
reconstructed result doesn't look like anything useful. 
Just using the average phase from the transform produces
something that looks like the average magnitude and zero
phase reconstruction, but with some extra lobes at the
corners due to the phase bumps near DC.  I decoupled the
correlation calculation from the phase calculation, and that
produced better results which might be a PSF candidate, but
which is shifted slightly in the frame.  The resulting phase
is smooth but has a slight gradient to it which is
responsible for the shift.  To use as a PSF I just shift it
so the maximum is at (31, 31).

I wrote C code to do the forward multiplicative
deconvolution search, and applied that to several frames of
a movie, and then used the resulting images to get better
PSF estimates for each frame, and averaged them all
together.  The SWRI alphas are not online, so I've been
running everything on the 2 Macs I have here. I used the 3
main PSF candidates (average magnitude and zero phase,
average magnitude and correlated phase, and average PSF from
forward deconvolution frames) to compare their performance
in iterated deconvolution (minimizing sum of squares error)
of several movie frames.  In all cases the 3rd PSF was
consistently better than the other two, so I am running
forward deconvolutions on more movie frames to get more PSFs
to average.  I modified the multiplicative deconvolver to do
additive (and subtractive) perturbation of images, and the
result is that you get an image, of sorts, but it has
negative values in it and isn't quite as good as the
positive definite image.

I'm currently using random band-limited data with compact
support to try to create an 'inverse PSF' to check out the
claim that deconvolutions can be turned into convolutions. 
If this works, it would mean that instead of spending a day
deconvolving each frame of data, we would spend a day
finding an inverse PSF and then all deconvolutions of that
PSF would become (fast) convolutions with the inverse PSF
instead.  I should know more about this next week.