When we repot cattleyas and other tall sympodial plants, it is important to keep them stable and unmoving in the pot while they get their new roots established. I have always used "pot clips", or "rhizome clips" - bent wire that grips the pot lip and provides support for the plant - but while that may work well for clay pots, I have tended to crack plastic ones.
There will be an article by David Grove in the AOS "Orchids" magazine shortly on a new way of managing the plants through the use of biodegradable rhizome anchors, but I thought I'd share it with you.
The key is the use of two biodegradable plastic t-shaped "stakes", which are used to hold onto a wire "U". Both the bottom of the main spear, and the tips of the bent-down top of the T are barbed, so they grip the medium really well.
You fashion an elongated "U" out of wire (David recommends the stuff you hang suspended ceilings with; cheap at Home Depot), loop it under the Tee, and with the wire running over the rhizome, you push the anchor down into the medium. Then you use a second anchor on the opposite side of the rhizome to apply the pressure that secures it.
I have tried it on a few plants this spring, and it works remarkably well.