Your thinking that they rank higher than you because they have more .edu links is flawed and a very poor conclusion especially since it is proven this isn't true. You're wasting your time.
@stymiee, i didn't say that this is the "ONLY" factor that caused my competitors to rank higher than me. But this is one. These .gov and .edu sites has a high page rank and linked to a million or even thousands of sites. Wouldn't you consider these?
Yes but not because of their domain extension. Those pages are obviously quality pages. That is why they have lots of inbound links (and thus high PR). But it has nothing to do with their domain extension. Your goal is to get links from pages with these qualities. Not pages with .edu or .gov file extensions. The former will serve you well. The latter will waste your time.
You did imply it though. Otherwise, why would mention them in your post? But it's neither here nor there at this point.