Hmm you could avoid writing to the depth buffer, where the billboards are transparent. Or if you sort them by yourself, you could use depth read and draw them from far to near.
Here’s the answer. I simply have to draw them in a different order, from the camera. I was under the impression that device.DepthStencilState = DepthStencilState.Default; already took care of that somehow, but it was made clear to me that this does something else.
So I just need to take all my objects and sort them based on distance from camera before drawing them. I was able to do this with this sort by comparison equation: