Well, nowadays "Hawthorne" has sorta branched out (pardon the pun) to include Belmont street, unless you're a hardcore traditionalist ... :-) ... so you've got a few more options there ...
Doing a cold move where you haven't even visited the area would make me a bit nervous, as even all of Hawthorne doesn't really look like Hawthorne anymore ... if you're going by what you find on the web I'm guessing the real "heart" of Hawthorn might be 21st up to 50th ...
Anyway, forget the apartment complex searches, you can find what you need at Craigslist:
craigslist: portland, OR classifieds for jobs, apartments, personals, for sale, services, community, and events
Just search in the Housing/Apts section, key word "Hawthorne." I don't know what prices are in Huntsville but I strongly suspect you'll encounter sticker shock when you see the rents, but still, it is Hawthorne. I'd also search on "Belmont," as it's getting almost as trendy and it's just a few blocks over (Belmont runs parallel to Hawthorne).
You might even search on "Clinton" street but that's on the other side of Division and has pockets of cool-ness and not-so-cool-ness. Good luck on the move!