From what I have seen, the gallery wraps do not need to be framed. They print is wrapped around the frame and gives it a nice finished look that can go right on the wall. That's not to say you couldn't put it in a frame though. I have also seen canvas prints on a streatcher frame where the print was not wrapped around the outside of the frame. It showed just plain canvas around the edges of the frame. Something like that I would want in a frame.

I order all of my frames through www.framesbymail.com. If you click on Metal Frames at the top of the page, you will find 2 types of canvas frames. One is a Canvas Depth frame which as the name implies, is pretty deep. Looks like about an inch deep give or take depending on the frame style you choose. I would think that a wooden gallery wrap frame would fit inside these frames.

The other type of canvas frame they have is called a floater. That site doesn't offer plexiglass, backing or matts for these frames. I'm guessing your idea of ordering the print on a double mattboard would work for this type of frame. Also, I don't think I would cover a canvas print with glass, or plexiglass.