I've attempted to model the spatial filter function as a gaussian (or PSF) plus an inverse gaussian. i.e., the high-spatial-frequency components are smoothed with the PSF, and the low spatial frequency components are convolved with a (1-gaussian) high-pass filter. First, the mildly good news: With a 300" FWHM large-scale cutoff, the filter PSD reasonably resembles the iterative map PSD:

Luckily, the double-filter goes a very long way in explaining the scale-free flux loss. In the following diagram, I show the effect of the filter compared to the input map.

The filter only recovers about 75% of the flux at ANY wavenumber. The map does slightly worse at high frequencies, which I can't explain yet. These show the recovery fraction of the iterative maps, a gaussian smoothing function with FWHM=33", and the mid-pass-filter. Map20 (no smooth) has a lot of additional "noise power" at high spatial frequencies; if it wasn't for the telescope filter function, we would apparently have pretty good high-frequency recovery. Hmph. Note that map20 is higher than the filter at some intermediate frequencies, but quite a bit lower at higher frequencies. Also note the moderately poor agreement between the 'smoothed' and 'smoothed (theory)' lines.

Finally, look at the comparison between map20 and fiiltered. The agreement is not bad for positive points; filtered is apparently slightly higher but that can be adjusted. The problem: the filter forces some structures that are negative or zero to be positive. For example, look at the feature at 210,300 that is negative in Map20 but positive in Filtered. In the real (input) map, this feature is lower than its surroundings - it is legitimately negative.