It took me a little more than three months from filing to getting my EAD through AOS (filed 4/15/16, EAD received 7/18/16). If it holds the same for you then you might not get it in time, but you'd only be out like a week or two. There's really no way to expedite the EAD request so try and talk with HR about possibly going on leave for a couple of weeks (it really shouldn't be more than that). good luck!