I think that the final song is about the changes that are taking place with the main characters. I think you're right that it's about emotion, but it's not about not having emotions but having strong emotions. We see Captain Hammer crying in a therapists office (It sounds like he's singing a verse to the song while weeping, something like: "I didn't mean to take her life, and now it hurts inside." Although I'm only positive about the word life and everything after that… the first part is hard to hear and understand.
Still… it's about emotions and how we deal with them… Captain Hammer is trying to work through them (albeit probably for entirely self-centered and self-absorbed reasons), where as Billy/Dr. Horrible has completely shut down his emotions… he is unable to feel anything because he's overwhelmed with grief. Stuff like that really happens… people cope with their emotions in a number of ways. Captain Hammer is seeking help, and Billy is bottling it up inside.. again they remain complete opposites of each other.
What I love about Dr. Horrible is how it's like Pie. I mean, you have the surface layer which is fairly obvious (and slightly cheesey). The surface layer is there for the people who don't want to delve into the deeper meanings.. It's fairly obvious what the story and songs are about.
Then you have the filling/meat of the pie (depending on the type of pie). This is all that space that the Whedon Clan left for us to look for deeper meanings and to find the depth in the songs and story. I half think that Joss would laugh at some of the things we think up, because some of the things that us fans come up with would probably seem amusing to him because he knows what it really means. The more room we are given to speculate and add depth to the story, the deeper we get drawn in. The best stories are the ones that leave the reader/watcher with just enough information to want more.
Finally you have the crust again (which, as any baker can tell you, isn't actually the same as the top crust, or how could you get the filling into the pie?). If you dig around deep enough into the filling you'll eventually come back to where you started. It's entirely likely that, at least on a few things, the things we see at the surface are the things we are meant to see. The meaning that is on the surface might be the real meaning.
Dr. Horrible is like pie. Mmm, pie.