If your university webspace supports PHP and MySQL, you should be able to install WordPress at /~(myusername) (or at /~(myusername)/blog, if you don’t want to create your whole site with WP but use it for a blog, only). Typically you don’t need root access for that. But in any case, you should probably ask your webmaster if it’s allowed to install and use it there.
This has been pretty nice because, even when the user clicks on links between pages or posts in the blog, the only thing showing up in the address bar of the browser is www.(universityname).edu/~(myusername), because the blog is constrained to a frame.
This is a bad user experience, because users can’t link to specific pages anymore (by copy&pasting the URL from the browser’s address bar).
Also, as you have noticed, that way the WordPress.com URLs get indexed, because your own page only contains of an iframe, which is “nothing” in the eyes of search engines. But you don’t have control over WordPress.com – the service might shut down for whatever reasons and then all your URLs linked all over the Web are gone.
Unfortunately, WordPress.com doesn’t support the canonical tag, so I can’t tell the blog to advertise itself as my academic URL in the header.
That would not help. canonical must only be used for duplicate or superset pages. However, your page (universityname).edu/~(myusername) is not the same as the blog at WordPress.com. If you use iframe with an external site, no search engine considers this external site to be part of the page the iframe is used on. Otherwise everyone could embed some nice pages via iframe and would get ranked for their content, too.