Since you aren't making any changes in play speed, subs are a piece of piss.

Rip them from the original DVD using PGCDemux. It'll give you all the files in .SUP format.

Do the intermediate muxing of your new video, audio and subtitle files in MuxMan (not many authoring programs can handle .SUP format).

Then of course use VobBlanker to drop your new muxed content back onto the original disc.

For x264 files try AutoMKV or MeGUI.

Those screenshots are not of the same frame, so comparison is a bit difficult, but, I don't see anything that looks like the work of a deband filter. Have you checked the cantina scene? The screenshot you had before of Han's hand has banding.