If you get different magnitudes of wavevector k, you are doing something wrong.
Your 32x32 grid, each point of it maps EXACTLY to the same point of original 256x256 grid. Complex amplitude on downsampled grid should be corresponding to complex amplitude on original size grid.
Downsampled grid is centered on spectrum center, so that downsampled spectrum will contain the same wavewavector magnitudes, as original grid, but only smaller than 2PI times sqrt(16+16), divided by patch length ( while original grid goes beyond that, reaching as high as 2Pi times sqrt(128+128), divided by patch length.)
That, in the end, effectively gets you exact copy of displacement field, but at lower resolution and without majority of short waves.
Any kind of spectrum logic or other settings need not be touched at all.