I did mine at work.
Look under "signs" in your phone book, and ask the people you call if they have a Gerber Edge.
If they do, then ask them if they print LexEdge on it.
It does have some limitations.
You can only print about 11-1/2 inches or so with it, but it will do custom cuts after printing to fit whatever shape you need.
Custom screenprinting (which is what the game companies used to do) is going to be REALLY cost prohibitive though.
There are a couple other options, if you find the right people.
1) You can have the image digitally printed on vinyl, and then overlaminated with a protective material (usually polyester).
That comes anywhere from 1-mil, up to probably 7-mil, but I don't know how many shops will stock it above 2-mil (the usual industry standard).
2) You can have larger stuff digitally printed, and then laminated with "floor graphic" covering, like what you'd see for floor ads at the grocery store.
That stuff works great, and is really tough; but, again, not everyone does it.