"and considering how many we have it's amazing our rankings aren't better"
I think you may be in the wrong mindset in all this
Remember that Google determines the quality of the backlink from the quality of the site. That can be determined to the reputation of the entire site or the page itself. Just look at JC Penny and it's faults. They are a VERY reputable company and they still screwed up.
Honestly whether it's a .edu, .gov or whatever else it may be coming from Google doesn't care, it only cares about the quality.
Just because you have a ton of links from a .edu really doesn't mean jack squat (TBH).
My .edu links never show up in my Google Webmaster Tools
Who knows, that could be for many reasons, it does not necessarily mean that Google does not already know about them and are not considering them.
Hope that helps