What you're really trying to do is build virtual albums. You want new art, the ability to sort like albums, and everything else that albums do. I understand the desire because I've wanted to do this also in some cases.
What I what I figured out, at the time, was that I really kind of needed to copy (or rename) the original files for each song, into new directories on disk, and then make new albums from those directories. This worked really well for me, but it's not exactly what you want. Because you might have 3 or 4 virtual albums that all contain the same original track on disk. So you'd have to make 3 or 4 copies of this song (file) in order to do it this way.
But there's another way that might appeal to you: Particles. If you make particles of each song you want in a Set List, you can then arrange those particles into new albums with the name of the Set. As an example, I decided to make a Set for Led Zeppelin's first TV performance. See attached screen shot.
I made particles of the 4 songs in the set. Then I highlighted the particles, opened the Tag Action Window, and gave them a new album name. Then I changed the cover art to another picture. Finally, I renumbered them based on their order in the set. The last song is wrong, but I wanted to include a song from a different album to prove that my "virtual album" could span real albums and real directories on disk. ...and it worked perfectly.
Particles have their own set of considerations of course. They sometimes don't rename correctly when doing RM&C. They also are part of a stack, so they get hidden when the stacks are collapsed. So this solution has it's own considerations. But it seems like a pretty decent one to me, at least after playing with it for 10 minutes.
Good luck.
Brian.