You should've worked with them on the song

You can’t cut songs from a musical without losing the plot.

But what if you changed the plot to compensate for only OP (and whatever few other good singers still remained)? And then even called it avant-garde perhaps???
[Or simply make all of the other Cats mute ie, naturally dis-inclined/ un-interested in their surroundings! Lol]

Actually songs are cut, or moved all the time in musicals. Usually when one is made from a stage version, into a movie. For example in The Sound of Music. In the stage version, the song My Favorite Things, happens near the beginning, and is sung by the Mother Abbess, to Maria. In the movie version, it's sung later by Maria, to the children. The plot isn't changed at all. In my opinion, where it's sung in the movie, makes more sense.

No wonder audiences are confused or feel shortchanged.

They might as well put a drum solo in Beethoven’s 5th!

Some you can

How about just having OP sing her songs anyway without the other "boat anchors," then have somebody narrate in the missing pieces? Could you turn that into some sort of new performance art genre perhaps even? Just swinging for the fences on OP's behalf....
Good luck, OP! :-)