The one you seem to be relying on is the last one, which usually in dictionaries means the weakest one.
Personally, I don't think that's a valid definition of the concept at all; I've NEVER seen or heard it used that way -- EXCEPT by gun nuts trying to pull what you're trying to pull. BS like that sometimes, alas, finds its way into dictionaries... Fortunately, though, at least it usually ends up among the last of the definitions, just like here.
I don't think the word "militia" means what you WANT it to mean.
("American Heritage", BTW, doesn't that sound kind of rah-rah-right-wing?)