for a mirror lens, we [or Samyang] know the geometry of the lens pretty exactly, and hence its point spread function.

The first part of this sentence does not naturally give rise to the second. Consider, for example, that most lenses have circular apertures (at least when wide open). Do the images from them all look the same? They do not, and the reason they do not is because they are aberrated. The mirror lens is no different.

Your second image, of the donut, is only a piece of what is often referred to as the generalized pupil function. That function is P(x,y) = A(x,y)*e^(-i*phi(x,y)) - you drew A, and have no knowledge a priori of phi. Your blind deconvolution algorithm, depending how it is constructed, may try to reconstruct phi. In that case, you really can compute the PSF and successfully remove its influence from the image.

However, there are two more issues. Your PSF array and pupil array are the same size, and the pupil extends over the entire array. This forces you into an aliased regime, where Q < 2, and your PSF is not faithful. You need to pad your pupil first before taking its Fourier transform.

the abs in your PSF also implies that the original PSF array is complex. The electromagnetic field in the image plane is complex, the PSF for this type of system is not. People either use the terminology of field PSF and intensity PSF, or coherent and incoherent PSF to distinguish the two. You seem to be modeling the field PSF, when you need the intensity PSF. Take the mod squared of the (properly padded) fourier transform of the generalized pupil function to get the intensity PSF.

If you have that, then yes, you can remove it from the image with no qualms of any sort, only a loss of SNR / increase of noise.

The defocused PSFs will need to be modeled independently, and that is more complicated.