How to Improve Keyword Rank?

So, busy work, not SEO.

.edu is not relevant; a page on a .edu site that's got no backlinks of its own has the same juice to pass to your page as a page on a .com or .net. or... that has not backlinks of its own.

It does not have to be in that niche... It has to be in any niche where you can create a post that will be accepted... on any topic you want...

If you can write a great article about reverse mortgages, I'll give you a link to your site...

Of course, you won't get traffic, but you get the link.

Things to keep in mind:
you can get a link so you get traffic... and, then, you need to post on a site that's got people interested in hosting visiting it

you can get a link to get SEO juice... and, then, you want your backlink to be on a page that's got lots of backlinks of its own that are not crappy links... at the very least, it's being linked to from such a page on the blog/site

or a combination, you want the traffic and the SEO juice, and then you want your link to come from a page visited by people interested in what your site is about that's got a bunch of backlinks of its own.

Look into the skyscraper and broken link techniques.
Create some awesome content on your site and start contacting site owners telling them you can create a piece at the same level and put it on their site if they link to it from their homepage.
Create some awesome content and contact site owners and see if they'd be interested in publishing it on their site and give you a link and link to it from their home page.

Why homepage? Most sites get a good number of backlinks to the homepage and none to very few to other pages.

Yup, there's work involved. But you're already working for nothing, so it shouldn't be hard to do this work.

PS If your site is about wedding dresses and you approach a mortgage broker, he/she/it/they would be harder to convince that you can produce mortgage content of sufficient quality.