Is there a better way to do this than creating a new c++ project and then migrating the content over manually from the blueprint one?
Every project is c++ and blueprint at the same time. There is no any sort of limitations.
It impossible to “convert” BP project into c++ because there is no such 
So, you can migrate blueprints from BP sample into C++ sample, but it’s not converting, it’s just asset migration and nothing more
However, what can be faster than “Select all => Migrate to another project”? Oo