Hi @rainfieldcn,
This isn’t a full answer, but to point you to a recent discussion about interpreting the anisomag matrix, its worthwhile to checkout this post: Help interpreting the anisotropic magnification matrix - #2 by mmclean.
After adding the identity and taking the singular-value decomposition (SVD), I believe the singular values would give you the magnifications along two orthogonal axes (major and minor). The angle relative to the image x-axis would probably be derivable from the rotation matrices (U or V) but I am not entirely sure if it would correspond to the angle relative to the x or y axes of the image.
Best,
Michael