Thank you for the replies. The folder structure looks like the following. The info between the { and } is what I added.
Music {main folder}
{Tons of individual songs <--These are what I want to organize}
ABBA {folder by artist's name; the rest of these are organized and I don't want to touch them}
The Definitive Collection, Disc 1
Songs for this album
The Definitive Collection, Disc 2
Songs for this album
Adele {folder by artist's name}
....
I'm currently using dB Power amp to rip the CDs, and have been using this for many years. This also adds the (not always correct) metadata for the CDs, creates a folder by artist and then by CD name. I was previously using another highly regarded program, whose name I do not remember. If I run into an issue, I use MP3 Tag to correct everything.
To re-rip these, I'd (a) have to find the CDs, which are in many, many folders in my basement, and (b) figure out which are not correct, and (c) re-rip those. Out of 816 albums, maybe 1/5th or so are not in folders. It's hard to know because I can't count the number of songs, and of course there are multiple songs per CD. Also, some of the CDs are ruined, as I used them in my car and scratched them/broke them/lost them. There are quite a few I could not replace.
I'll try one of those programs and see what happens.