It may well be rootbound, but what you've pictured is more "overgrown" than rootbound. As fralexandr notes, the fuzzy things are "rhizomes", not roots.
I tend to agree with the idea of just starting new plants from the most recently grown rhizomes that are actively growing foliage, taking a chunk of the rootball along with them. But if you like that "Cousin It" look and want to keep it intact, the rest of his advice is sound, too, though I'll add that ferns, the roots especially, but to some extent the rhizomes too, can attach pretty freaking tightly to porous pots. If it seems to be seriously stuck on there when you start trying to pull/pry it after soaking, you might consider just cracking the old pot, removing whatever big shards of pottery you can without ripping away a huge amount of the existing rootball, gently pulling the old rootball apart a bit with your fingers (without actually ripping it wide open) and then burying that whole business in a new pot with as much fresh soil as needed to fill in the spaces you've made by loosening things up, and the rest of the space in the new pot. ETA: It might dry out a little faster since the pottery won't hold as much water as soil, but new roots will just grow around the old, broken pot and it won't really interfere with the plant's future growth. (Just plopping the unbroken pot in a new one wouldn't be a good idea, though.)
Also, I'd look for a shallower pot to move it to. Those ferns don't tend to grow very deep roots, so overall, a bowl-shaped "planter" will work out better over the long run... ETA: It should be at least as deep, or a little deeper, than the current root ball, but not much more than that.
PS: You can just toss it in a big bucket, sink, or even the bathtub if necessary to soak it. Being fully submerged for 20-30 minutes won't hurt it a bit and by now, every bit of loose soil will have been pretty thoroughly tied up in the old roots so while it's intact, the soil isn't going to float out of the pot/away. (Though if you do use a sink or the tub, do put a screen or something over the drain, since as you remove/deal with the old pot, miscellaneous dead roots/old soil will work loose and you don't want to clog the drain.)
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