Wow, lots of questions! I'm a little surprised that B6 and BA do not have an interline agreement, particularly given B6's recent alliance with AA, a BA partner. I think you should double check your info.

Where are you originating from? If from the DC area, consider flying AA to JFK. They certainly interline with BA, and you could purchase a day pass (which includes wifi) to use the AA lounge at JFK upon arrival without exiting the secure area.