Have you considered the Council of Literary Magazines and Presses? It might be a good place to begin.
I don't have much experience on the periodical end of things, perhaps someone else could advise?
From their
website:
The Council of Literary Magazines and Presses serves one of the most active segments of American arts and culture: the independent publishers of exceptional fiction, poetry and prose. Literary magazines and presses accomplish the backstage work of American literature: discovering new writers; supporting mid-career writers; publishing the creative voices of communities underrepresented in the mainstream commercial culture; and preserving literature for future readers by keeping books in print. 
Forum
