It seems inelegant to me to split this into two different modules, one to include, the other to extend.

Trust this answer. This is a very common idiom in Ruby, solving precisely the use case you ask about and for precisely the reasons you experienced. It may look "inelegant", but it's your best bet.

When we usedef self.method, though, we are defining a method across scopes: we are present in the regular class scope, but we use Ruby’s ability to define methods upon specific instances from anywhere; self within a class definition is the Class instance we are working on (i.e. the class itself). Therefore, usingdef self.method is a leap to another scope, and this feels wrong to me.