Not 100% sure I understand about the "delta functions". I guess if the edge rolloff is totally monotonic, and quite extreme, then the pixel grid acts to quantise a function that goes from 1 (in the bulk) to (1 minus something significant) in the last row. I guess this is what you mean?
I'm amazed that the field would be so flat as to work like that, but maybe this is the case. If that is the case, the corner amps should look very different with respect to wiggles, as they have a lot more edge (by a factor of 5x). Do we see that to be the case?
I still think that given just how clearly separated these wiggles are (i.e. nice separate peaks on the histograms) it would be really interesting to plot each wiggle, one by one, spatially, to see just how they look. If your theory is correct, it should show up as neat bands, each moving in as you go up in wiggle-index.