I use Midwest. They've been more than willing to accommodate. Sometimes they've even able to fit my order in a flat rate box and then refund me the difference in shipping.
That being said, you're almost always going to pay more for shipping to APO fom anywhere.
Also, if you ever encounter someone who wont ship to APO and can't find it anywhere else, use Ship It APO. They will forward the package to you for a small fee. Cheaper to use family/friends, but not as quick as Ship It APO.