Managed to do it by using the same technique that's in the example project "3D in 2D". Took me a bit to figure it out, but it worked. Or in other words, I'm making the game 2D, but with some 3D models in it.
On a related note, I could've made the camera orthographic at first, and then simply use static models to block movement. Since the background is just stars and/or planets, you don't even notice the difference between perspective and orthographic. But I don't mind making 2D sprites, so I'm fine with this.
Just in case you're wondering what the hell do I want 3D models for in a simple space setting, I needed things to be orbiting planets, and I'd have to represent that either with still imagery, a long 2D animation of a slowly rotating planet, or a camera rotating around a 3D planet. So I managed to get the latter. :)
Thanks for all the suggestions. They did help, even if indirectly.
