When I repot an oversized catt, I start by filling a 5 gal bucket with water. I add a little fertilizer, and fungicide.
I soak the plant in the bucket. Sometimes for a couple of hours. Normally the roots that are clinging to the outside of the pot can be gently worked free. They are much more pliable when they are completely saturated.
Then I work the plant out of the pot. Sometimes the pot will be sacrificed. I use a hose to wash the roots free of any potting mix. If necessary I will cut dead roots.
If I'm thinking of making a specimen plant I will move from a pot to a basket. I use landscape fabric on the bottom of the basket to keep the mix from falling out.
I use a large mix of aliflor, charcoal, spongerock and large bark. Usually I can work the mix around the roots to a point that the plant is secure, if I feel that the plant is too loose then I'll work a piece of bamboo under the top basket slat, over the rhizome, and then under the basket slat on the other side.
Here are some photos of the process, although on this operation I did divide the plant a bit.