Birch are a little tricky to get to backbud but not impossible. The main thing is the timing and the health of the tree. *I would pot it in a large training pot next spring and let it grow wild with a heavy fertilizer program all season. The following spring chop the trunk right when the buds just begin to swell. All of the root reserves will be looking for dormant buds to put their energy into and you should get new buds further down the trunk.

Tony