I bit the bullet and figured out how to linearize and fit a reasonable set of WCS parameters, and how to reinterpret the fit output as conventional WCS parameters.
The basic idea is to treat the tangent plane choice as a separate thing from the relationship between x,y in the image and ideal u,v coordinates on the tangent plane. So you fix the tangent point (in the image and on the sky), and then fit for the relationship between x,y and u,v on that fixed tangent plane. Then you re-interpret some parts of the solution as an adjustment to the tangent point on the sky (you don't want to change the tangent point in the image because sometimes that is known a priori). Then you iterate, starting at the updated tangent point.
I started to write the code. The most difficult thing was to figure out how to interpret fit output coefficients in terms of the standard WCS parameters.
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