I just got off the phone with a lawyer and based on her interpretation of the law I will need to pay through the month of April and most likely a pro-rated amount for five days in May. Though this is the legal interpretation, she seemed to think if the leasing agent was a true red-blooded American then they would call it good the day I hand over my orders.
Since I have fulfilled only a portion of the notice requirement (have given notice but have not yet supplied orders) then the "30 days after notice has been given" portion of the clause will not go into effect until the day on which I hand in a physical copy of my orders. Which means the lease won't terminate until May 5th. As you guys already pointed out, she called BS on the leasing agent trying to stick me (sts) with early termination penalties.
Paying through April is definitely not ideal, but it beats the hell out of forking over $3k.