Ok, lets try to work together to get this figured out

According to my research, there are several International Airports to fly from (for Eastern/Midwest US)...
Miami <-- THE most popular city for direct flight to BGI, other Int'l airports often have connection here
Atlanta
JFK NY
Chicago
Houston
Charlotte
Pittsburgh
Philadelphia
Boston
Cinci
St Louis
DC
Toronto

Most common airline I keep seeing with cheapest flights is American (or Air Canada)

Two main arrival times into BGI, 2pm and 10pm.
.

Here is my own personal dilemma.... Our reservation at CB is from THURS 8/1- SAT 8/10. Now, I'd really like to arrive at CB in the afternoon. Problem being, I would have to add on a date to our reservation and arrive 7/31, or arrive on 8/1 at 10pm (and I do not want to pay that much to enjoy the hotel maybe for an hour!) I'd be more likely to arrive at BGI 7/31 10pm and sleep in the airport and get to CB bright and early on 8/1

Now, we do not mind leaving our departing city (we are VERY open to this, will drive or take train or fly, anywhere within 300-500 miles of mid Michigan) on 7/31 and staying overnight somewhere in a connection city 7/31 to arrive at BGI in the afternoon on 8/1.

I REALLY wish there was a way to say: "I want to arrive at BGI on 8/1 at 2pm - where (and when) should I leave from to get the cheapest flight?" ....

Please, if you've already booked, list your dates and departing city > connecting city (or cities) > arrival time at BGI. And, Id appreciate a price range of what's already been booked...

Thanks!!

Kelly and Derrick