Hey Floyd: What you are describing is more commonly known as phenolic or micarta. That is tought stuff, I use it for motor mount pads. I have used it for horn pockets, but have changed to spruce or bass because it is much easier to sand and shape into flap tapered cross section.
I hate to disagree, but FR-4 is, indeed, an epoxy-glass laminate. You can get phenolic circuit board material. It's often used in really cheap consumer electronics because it's -- well -- cheap. But epoxy-glass is quite common, and is to be found anywhere that the circuit board quality can make or break the product (I doubt that you'll find a phenolic circuit board inside of a PC, for instance). Phenolic is used in things like cheap radios and electronic alarm clocks; it's mostly restricted to far east manufacture these days. FR-4 is what you'll usually find as surplus copper-clad board in the US and probably Europe.
I hear you about your material choice -- I'm currently making my very first pair of lucky boxes for a V-tail; I'm using FR-4 because that's what I have around and I know that I won't have to worry about strength. But I'm not looking forward to getting any exposed corners to look good.