Small status update;
Part 1 has been color-matched and upscaled. Of course it isn’t the same quality as HD, but it looks quite okay when color-matched.
I experimented with several options (color-matching prior to upscaling, adding noise before/after color-matching) and I seem to have found the result I like best.

So right now it’s this:
-Upscaling and adding grain first,
-Color-matching in AfterEffects after that.

Next week I’ll try to get Part 2 done. Though I am still missing the end credits for Part 2.