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Wow, that is something. You've done well with it.
The one I see is a hybrid Phlaenopsis. If the other is also, keep in mind that even if you cut off all the roots, they will probably recover with decent care. Of course you don't want to do that, but that knowledge will keep you from being too timid.
I'm guessing most of the healthy roots are outside the basket, but I can't be sure of that. The moss deep inside is probably rotting. I would probably try to remove them from that basket, and pot them up separately.
To do so, put the whole thing into a water bath to soften up the moss, then try to pick out the moss a strand at a time. It will take a long time, and you don't need to do it at one sitting.
Then you might be able gently to lift the plants out of the basket without damaging the roots too much as they come up though the holes in the wire frame.
Once liberated, soak the roots in a bucket until they are very wet. They will be more flexible. Repot the plant separately into the smallest pots that will hold the root systems. Use any medium you are comfortable with. For Phals this size, people use medium to large bark chips; LECA clay balls; horticultural charcoal chunks; large particle horticultural perlite; and combinations thereof.
If you haven't read it, this thread gives some good information on growing Phalaenopsis:
The Phal abuse ends here.
It is accessible via the left yellow menu, Forums; near the top select Beginners; and you will see it as a sticky thread near the top of the listings.
Repotting from wire-wrapped moss pots?
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