It's 9x13, to be exact. I sort of think otherwise...
I have made a quick mockup of four sprites that have the same dimensions of the number box, a Cyberdisc, a Snakeman, an Ethereal and a Muton.
The first attachment shows the icons as their original format. Yes, you are right, it is not much space to work with and it ends up being small. But it seems, at least to me, the windowed mode has doubled the pixel size, effectively making it look something like what I have in the Second attachment.
Keep in mind however that some people play OXC Fullscreen, and sometimes they have stretched the viewscreen to fit. That effectively makes those number boxes even bigger than before, so I think, even though it is somewhat limiting in pixel art, you will definitely tell which alien is which in those number boxes. You could even pair that with your current mechanic of "Current soldier sees alien vs Other soldier sees alien!"
Granted, there are also modded alien races, and since OXC doesn't recognize them as vanilla, they won't have a corresponding "detected" icon, so that would be when the numbers come back. Of course these icons could be added as extraSprites in a newly made ICON.PCK folder or something via Ruleset.
The Implementation may require a bit of graphical work, but the coding part seems somewhat easy (at least to me, anyway).