I've been contemplating doing the same thing, except was thinking of using parallel linen threads along the bow axis as suggested in The Traditional Bowyers Bible Vol. I instead of a thin flat piece of cloth. This is a hickory self youth bow that I lifted a splinter on during tillering. Bonded it back down, but want a bullet proof backing obviously.
Hopefully not a hijack, but what are the ways folks are using to put pressure on the backing when using long parallel threads while the glue dries?