Echoing other people's comments, I think the bounded campaign can be a really fun thing. As you say, it lets you focus on telling a single compact and integrated story, rather than "whereever this wanders off to." I've had some success combining a story limit with a real world time limit. For example, one campaign I ran was defined as being 10-12 roughly monthly sessions over the course of one year of playing time. Having that deadline kept me focused on advancing the story, and helped prevent bloat. I think that made the game run more smoothly.
One thing that I would suggest is being less fixed on what the subsequent stories are--this may not be your intent, but it's the impression I get. For example, if story 3 isn't a huge success, you may not want to continue with those characters for story 4. Or if story 1 is made of win, you may want to add a story 2 (or a story 3) that uses the same characters as in story 1, but gives them a different story/new set of goals.