Just realized, I don’t have /common/home since I have an SEO module that just rewrites my site to example.com.
I am actually thinking of removing the OpenGraph code from the header. Then just adding one instance of the code (with the correct default image) to home.tpl and another instance of the code to the product.tpl file.
Would that work?
I just want a default facebook share image for the homepage, and the product image for the product page (second one works fine by default).