I've had a lot of fun doing daytime DXing right on the Gulf here on the west coast of Florida and on the east coast at Dayton Beach.
Over here, right out on the Gulf, WWL and WLNO from New Orleans come in loud and clear all day at almost 500 miles away.
My most distant daytime AM catch with a confirmed ID is KTRH from Houston at 775 miles from the beach in Dunedin, Florida.
The louder station on 740 is WYGM from Orlando but at the 12 second point in the video, you can hear the KTRH ID.
http://www.youtube.com/watch?v=2WcH0JN1irg
The reason I mention WQAM is because it's at the low end of the AM dial where stations go greater distances on the land/sea path than do the stations on the upper end. Also, their transmitter is located on Biscayne bay according to Radio Locator which gives the station a clear advantage for saltwater propagation.
There's also nothing but ocean between there and the Jersey Shore beaches. If the radio is facing Miami, it should be just about in the perfect null of WFIL.
It's a long shot, I admit but it also doesn't seem out of the question.
There's another person here who has done daytime AM DXing from Bermuda with amazing results, getting many stations from the US east coast. I've heard many of the audio clips too.