I've taken apart a few TVs, but I'm certainly not a repairman or anything. If you are careful and observant you should be able to de-case a TV's innards fairly easily. The TVs, and most monitors, I've had in pieces have metal brackets at the corners of the tube for mounting to the plastic casing. This is typically all that is holding the tube to the case.
I have used these metal brackets to hold my screen tube to a plywood board (with the appropriate hole cut in it for the face of the tube to stick through) as a mount in my cocktail cab. It's sturdy as can be.
The arcade CRTs I've seen have much the same set up, but with a metal L-bracket system bolted to the corner supports, and the screen electronics attached to the bottom of the "L."
You could make a wooden "L" for the tube and electronics of your TV, and mount the "L" inside your cab.