Submit to campus and community publications as well. You'd love to see that sestina of yours in print, I know, but don't look down your nose at the prospect of writing articles for the campus newspaper, press releases for your club, etc. The point is to get yourself into print. Find a part-time job that requires writing or communication skills of some kind, whether it's writing news copy for the campus radio station, editing classified ads for the campus newspaper, or doing research for a campus department or program. When employers see that you've been paid to write, they start taking you much more seriously.
Universities produce tons and tons of writing.
And someone has to write it, edit it, or both. There are journals and other official publications, of course. Whether or not they're hiring, look into the possibility of volunteering your services. Giving a few hours a week as an unpaid proofreader , copyeditor , or editorial assistant will show an employer that you have real experience in publishing. Departments and programs of all kinds produce newsletters, reports, etc.