Now I have some data supporting my hypothesis that DSS wasn't interpreting the RAW data files correctly (thanks to Tom.G!). Here are two linescans comparing the 'old' interpolation method ('Bilinear Interpolation') and the new, *correct* interpolation method ('Adaptive Homogeneity-Directed (AHD) Interpolation'). No flats were used during stacking- these images were acquired at f/4.
The stairstep effect is completely gone now (the background is a lot flatter, as well). I used the original RAW files, not 16-bit TIF images. The DSS 32-bit histogram looks identical- this problem was really subtle...
Ok- regarding my comment about 'stacking invalidated the flats'. Last year (or so), when I got more serious about flat field correction, DSS generated a whole range of Master Flat 16-bit TIF files and then I deleted all the original RAW files- I figured, why keep 100GB of files when I don't need them anymore? What I didn't know is that the Bilinear TIF interpolation from DSS and TIF interpolation algorithm from Nikon's Capture NX program created differently-sized pixel arrays. Consequently, DSS simply ignored the flat file when stacking 16-bit TIFs.
Worth noting, once you have 16-bit Master Flats, you can manipulate them to improve performance- that's how I generated multiple master flats to eek out that final 0.01% difference: for example, I generated a series of mixed Master f/2.8 and a Master f/3.5 in different proportions (75/25, 50/50, 25/75). The RAW flats do not have to have the same image parameters as the bright images- however, all the RAW flats have to have the *same* image parameters (I can't mix and match different ISOs, for example).
So, I'm happy to report that the major problem has been solved (thanks, everyone!). Since I'm teaching QM this semester, I'm calling this 'first quantization correction'. Last night, I took some new RAW flat images and today will generate new Master Flats with the AHD interpolation method ('second quantization') and see how that impacts my low f-number images- presumably I won't have to contort the flats so much anymore. I'll post results in the usual thread rather than this one.