If you have a big enough piece of fabric I would mount the finished piece using a pre-stretched artist canvas. (Think modern paintings where the artist paints the sides of the pre-stretched canvas and then doesn't surround the piece with a frame).
Hummmm...interesting idea to stretch it over a canvas. I'd have to find a canvas exactly the right size, but it could possibly work. I've seen youtube tutorials where they mounted stitching on top of a canvas, but not one where they stretched the work over the sides of the canvas...so that would take some figuring out. My only concern is that this is a big, intricate piece which will likely take me many months to stitch, and if I ruin it in the finishing I'll probably cry.
Still, it's an interesting idea to consider and I thank you for it. I might try it with some cheap, non-stitched fabric first to see how it goes. If it works out it could save me a crapload of money in future finishing costs.