Would you use a spray like 505 or something stickier?
I never thought of doing that, but I seem to remember a Fons & Porter episode where one of their guests used spray adhesive to hold fabric in place while doing foundation piecing. As I recall (and I'm getting old so my memory isn't great!) they had a little box that they did the spraying in so it wouldn't get on everything else.
If it works well, it would be a big money saver, too.