My descreening process doesn't remove detail. If anything, it retains pretty much all of the detail that exists in the image. It starts with a fourier transform algorithm, which preserves as much detail as possible.
The second pass, a carefully-tweaked surface blur, smooths out the gradients while leaving the important details unchanged. This is capable of losing detail, but I tweak the settings carefully to target only the smooth gradients.
The third pass is a manual run with the blur tool done by hand. I completely avoid the detailed areas in the third pass.
Getting the gradients as smooth and soft as possible is important because any moire that's left over for the printer's raster image processor to process results in a dithered mess. Putting scanned halftones into a RIP that does its own halftones always results in a mess. This isn't ideal unless the desired texture calls for such an effect.
The print came out very nice, considering the printer is a low-end Brother MFC-J805DW. It would look a lot better on a high-end photo printer. Here's a 1200ppi scan of the print, with select portions showing the unedited original for comparison:

Full-size here:
https://i.postimg.cc/KGD24r7V/snes-aof-1200out.png?dl=1I'm going to print it on high quality settings now to see if there's a noticeable difference.