WOW! Those are absolutely outstanding roots! Congratulations! she obviously loves the conditions you are keeping her in.
I don't know if I would 'dare' change her from a clay pot to a plastic one?
I'm not a cattleya expert - my feeling would be to just 'sit' him/her
into a bigger clay pot as you say; using same mix and not mess with the roots?as they just look toooo healthy to be "messed" with.