The majority of the past week has been dedicated to debugging; it looks like cross-scanned simulations finally work. The plot below is a derivation of the spatial transfer function for a number of different intrinsic sky power-law power spectra.

Justifying the above plot is essential. First, the very steep power-laws [-3 in the example below] show a recovery fraction >1. This is simply because their S/N was inadequate - the output power spectrum is nearly flat, but at a level higher than the sky.

Second, the most plausible power-laws [-1.5 in the example below] show pretty good recovery (90-95% over the relevant range):

There are some "white" power losses, particularly in the flatter power-spectra. My best guess is that this has something to do with the relative scales being offset from a mean of 1, but so far all tests to show that that is the cause have in fact shown no problems at all. What else could cause a scale-independent power loss? Also, the flat power spectrum (and inverted) aren't quite flat because I impose a "galactic scale height" on them. Should I stop doing that?