If it's the perfect thing, just work with it! Sounds like you have gotten good suggestions for stabilizers. I used something called French Fuse to stablize the back of T shirts before quilting. It's actually a very light fusible knit.
As Tim Gunn says, "Make it work!". I'm sure it won't be as bad or as hard as you may be expecting. And what a cool quilt this will be with the map in the center!