I now know why most space-based games don't try to include multi-star systems in anything approaching a realistic manner. Whew. The following star system types are now available:
Binary center: 2 stars tightly orbit each other at system center with mutually shared planets.
Binary orbit: 2 stars orbiting each other further out, with planets around each individual star (or no planets, if they're in the "dead zone" of about 3 - 30AU which stops planet formation).
Trinary center: 3 stars tightly orbit each other at the system center, mutually shared planets.
Trinary, binary center, single orbiter: 2 stars together at the center of the system, with a single star orbiting farther out. Planets potentially around each grouping.
Trinary all orbit: 3 stars, one at the system center, 2 more in their own, independent orbits. Possibility of planets around each.
Quad center: 4 stars at the system center, mutually shared planets.
Quad binary center, binary orbit: 2 stars at system center, 2 stars orbiting each other further out. Planets possible around each grouping.
Quad binary center, single orbit, single orbit: 2 stars at system center, then 2 independently orbiting stars further out. Planets possible around each grouping.
Based on the system type, the masses of the stars present, their radii, and the orbital distances of the stars, I calculate approximate regions of stable planet orbits around each star/group. If I wanted to do this accurately I'd use some sort of dynamical simulation, but that would be a bit crazy given that this is a computer game. I have enough detail as is, so I fudged the calculations a bit. For systems with just "center" stars, it sets the minimum stable distance at the largest center star's radius plus 0.05AU and the largest stable distance at 100AU (arbitrary, but approx. the maximum distance of Eris).
For systems with stars in separate orbits, it gets a bit more complicated and calculates the stable orbit zone around each star/group as a mass-weighted fraction of the distance from the star's surface to the zero-gravity point between each pair of stars. I won't go into the details here, but I've been getting decent numbers out of this for multi-star systems.
In the process of setting this up, I noticed some errors in my star building routine that were creating nonsense values for the parameters of certain star types. I had to go back to the source I took some of my equations from and discovered that his paper was full of typos! That's the last time I trust something published in the Journal of Serbian Astronomy... probably should have seen that coming though :). I've since fixed the star creation routine and have confirmed that all star parameters are within expected boundaries.
Now that I have my stable orbit regions, it's time to build the planets! Gas giants are apparently key here, so they're going to be put in first and their characteristics will determine where/how many rocky/icy planets are created as well.