This might be an oddball suggestion, but I would take a look at Shock: Human Contact, which is an in-depth varient of Shock: Social Science Fiction . It's an unusual game in its focus, style, and mechanics, but it allows focus and attention to the hard-SF element, in a way that's quite unique (and doesn't actually require any astrophysics calculations, unless you're absolutely slavering for 'em...).
It's an indie game, and while I won't explain the entire system, it's got two fundamental mechanics I think will interest you:
Shock Ownership: One central tenet of Shock is that the game is defined by a small number of, well, "Shocks," which is the game-term for major SF elements. So "FTL Space Travel" could be a shock, as could "Uploaded Consciousness" or a new alien race.
Here's the cool part: each Shock is "owned" by a particular player. That player is effectively the GM or the arbitrator for how that particular science, technology, or race works. So for every major trope you use, you've got somebody who's actually in charge of keeping consistency and rigor - which is exactly what you want! And then, yes, the game focuses on the particular Shocks you've chosen, and you can expect the game to explore those ideas and technologies.
Minutiæ Contribution: A common occurrence is for somebody to add "Minutiæ" about one of the Shocks - basically, to contribute a new wrinkle or detail about it. (I won't go into the mechanic of when precisely this happens.)
This doesn't force your science fiction to be hard ("My Minutiæ is that FTL travel is actually powered by burning unicorns for fuel!"). What it does do, though, is shine a spotlight on the details of your SF-nal tech and science. Instead of everything being hand-waving and SF-dressed magic, there's constant interest in the details, and I think this meshes very nicely with your desire for a hard SF feel to your game. A game that's interested in these details will, I think, feel tightly bound to small details, and how they can have big and unanticipated effects. That feels a lot like a hard-SF flavor to me.
Shock is an indie game; Shock: Social Science Fiction provides the basic framework and mechanics (which are extremely versatile), whereas Human Contact adds in a specific setting, a lot of specifics and Minutiæ, and a particular structure very appropriate to creating a campaign of linked Shock games. The theme of Human Contact is an exploring society making contact with far-flung colonies, which split off from Earth long ago.
You could certainly adapt your own setting to the Shock mechanics. Alternatively, if the other elements of Shock don't appeal to you, you might try to lift the "Shock Ownership" mechanic into some other system, where it might add great flavor.