DrDre said:
… there’s some smoothing of detail, but I guess it’s either that or unwanted artifacts…

With this being only a proof-of-concept, I tend to push things a little further for the effect to be obvious. You can dial it back to your liking. Or use something different. For example, as these artifacts are actually enhanced noise, they would be different frame to frame. That might suggest using stabilized temporal averaging including one frame (or more?) on either side (image-block tracking handles in-frame area-movement). (Avisynth has such filters.) Then apply a milder application of JPEG Artifact Removal's Avisynth equivalent to keep more detail, perceived or real, while still reducing the remaining “out-of-place pixels” noise.

(All this is would be so you’d have the source in the best condition for your regrade to work it’s magic without it being wrongly influenced by things such as color-noise or crushed/blown areas.)