However, then I realized that I could prevent these issues. When I was washing my second roll of this film (the Ilford archival method), the water came out cloudy, each time I replaced the water. When I took the film out of the tank, I saw it was covered in a milky scum; I removed this with a sponge, and that roll of film had no issues with the fog, or with the numbers seeping through. This fog was also quite grainy; and thus this step will effectively reduce the size of the grain on scans!
I predict, then, that the fog-and-numbers problem is that the paper backing leaves a deposit on the film, which, unless sponged off, dries; and interferes with scans of the film, producing bad results. Washing it off eliminates these problems.

I am a bit puzzled here. Are you developing with the backing paper attached or is the backing paper leving deposit before you even unpack it?

Nice scans, i like what I see!