Repotting from wire-wrapped moss pots?

[Rheeseling]

Happy weekend everyone! New poster here, and very amateur orchid grower, so apologies for any terms I get wrong.

I got this arrangement of two different orchids (can only see one from this angle) as a gift at least 5 years ago which came in some sort of a moss-based medium wrapped in wire to resemble a basket.

By random internet reading and sheer luck I have managed to keep them alive and even get them to re-bloom every year (without repotting...eep), but the roots are obviously spilling out more and more and I'm sure they could use repotting. I just don't know how to go about it when the medium is sculpted/packed like this. Should I just plunk the whole thing in an even bigger pot and fill in new mix around the roots? Or have people had experience cutting apart/disassemble the basket? I am afraid of just tearing the entire base apart, roots and all.


Or is this just a lost cause?

Thanks for any advice you may have,
Rheeseling