If the trip is in June you don't have all that much time because you can't wait till the last minute to check for award availability. Have you done that yet for the three tickets on AA? In fact, you might end up having to put one person on another flight, anyway, unless you have something else we can use fairly quickly to get you the other 60k Advantage miles. (A good thing would be 200k Marriott Rewards points .. any chance you have them?)
There's a very easy way to get 30k DL Skymiles, Apply for the DL/Amex Gold Skymiles card (annual fee $85) with the 10k bonus plus an additional 10k bonus after charging 10k within 6 months. The first 10k posts within a month or two, but it takes time to get the rest of it, but that 10k can be added to anything you already have in the skymiles account and transferred at a 2:1 ratio through Diners Club to AA.
Others have reported better Citibank/AA bonus offers than I listed above. (10k + a companion cert .. look into that).
Do you have other miles or hotel points that can be used for this trip? There's often interesting ways to transfer miles around (usually at a loss), but you might have stuff you don't know can be transferred at a decent ratio. Somebody with all those miles probably does travel a lot, so I would be surprised if there isn't other stuff that can be used here.
Let us know what else you have and we'll see what we can come up with.
-David