You know, that's quite a challenge. It might depend on the needs of those asteroids. Have you tried imposters?
I tried DGDK Imposters (sold here at TGC site) to see if I could incorporate it to my project. It worked but I found some lacks for my needs, like that the imposters objects could not be shadered.
I use different regular meshes for MPL3D Solar System asteroids game, but that is because they are a few.
However, this allows me have total control over them, giving them higher detail and the feature of being divided into smaller asteroids when crashing between them or when they receive a laser impact.
For asteroid belts, I use meshes that contains several asteroid objects, so they can be placed and controlled all at the same time.
I think you are pointing right with the algorithm. Perhaps you could use some kind of hierarchy to not to render all asteroids at the same time.
[Edit: I didn't read the DX11 thing... maybe I've been too much disconnected
]