Veterans are a difficult bunch to reach, and a small article in a publication might just do the trick.
Actually, I'm not sure your correct. I think what is more important is that you are clear about what it is you're looking for. I have skills that I apply to non-profits quite regularly. But they are applied with an understanding of what is required and why and how my time, knowledge and experience will be applied to benefit others.
Otherwise, it all seems like a bit of a crap shoot... (Sorry for the American analogy).