We can instead mask all but the faintest 10% of pixels, and then subsequently add more pixels to the MLE until the DGR converges. See Section 4.3 of the Planck et al. (2011) paper.
These are some of the resulting likelihoods. There is a positive intercept! I’m not confident in these results, I need to consider more the order in which I mask during the iterative masking stage.