You are correct the damage looks like the bronze birch borer (also a tongue twister) and right now during the summer the only treatment is to fertilize the tree with a slow release food like Osmocote to help it outgrow the damage. Birch trees are very susceptible to this beetle that infects the tree in the spring by laying eggs in the lose bark. Early spring is the time to treat the tree with an insecticide to keep the beetle from laying eggs. The one birch tree that shows some resistant to the borer is the native birch tree. Birch trees like lots of moisture and fertilizer and do not like to be pruned as this encourages the borer. Just remove any dead wood in the winter if you must prune. Give the tree a few years and it if keeps declining cut it down. Sometimes a mercy killing is best so that an insect attracting tree does not attract more problems to your property. Keep growing, Marianne Binetti