I'm not one to be contrary for the sake of it, but you're asking for MusicBee to do something with a file and then never show it to you again.
It's so specific to this one use case and utterly confusing to anyone else that I think it would be a bad thing to implement as requested.
Lots of people have enough problems understanding how the "library" works already without providing fuel for a new stream of threads asking "Where did my music go?".
The other thread did suggest using a filter instead.
Given that you aren't deleting these files - because you want them available on other machines - something like a custom tag that you use to flag tracks you want to see when DJing seems a more elegant workaround.
Bee excellent to each other...