When people say moral theory, they mean the procedure(s) they use to generate their terminal values (i.e. the ends you are trying to achieve).

Understood, thanks.

I'm not sure that the consensus here is that all moral theories are unfalsifiable (although I believe that is a fact about moral theories).

Let's go with what you believe, then, and if the consensus wants to disagree, they can chime in :-)

Thus, one reason to discuss moral theories is to determine [as a descriptive matter] what morality one follows, in some attempt to be internally consistent

Are you saying that moral theories are descriptive, and not prescriptive ? In this case, discussing moral theories is similar to discussing human psychology, or cognitive science, or possibly sociology. That makes sense to me, though I think that most people would disagree. But, again, if this is what you believe as well, then we are in agreement, and the consensus can chime in if it feels like arguing.