Those clear slotted pots with lots of holes on the bottom are what I use to pot all of my orchids in. I like them for lots of reasons, but having lots of places for roots to escape is one of the built-in hazards.
When I repot, if I have one with roots similar to that (though I admit I've never had one with that many!) I do as Roberta suggested. I cut the pot off, very slowly and carefully. I use a sturdy pair of scissors, in my case kitchen shears. The idea is to damage as few roots as possible, though a couple usually end up getting minor injuries.
Yes, I hate cutting up a good pot, but as Roberta says, compared to the value of your orchid, pots are cheap. I would definitely not cut all those roots off that plant at the next repot as you mentioned.