Hi,
Birchbark makes excellent backing! Lots where I live. It's better if you seperate it right away, rather than letting it dry first. It seems easier to seperate the layers when it's still a bit "green." I've used it both thick and thin, glued on with TB2 or TB3. I think a thick enough layer would resist a splinter lifting on the back. The trick for me is getting pieces long enough and of good enough quality to back a limb.