One day Delta and Virgin will stop acting like they are two separate airlines and get their a**es in gear. It's all a charade to fool the US Government that they don't own more than 49%.
It sounds like Vayama did a separate sell entry when they reprotected you and ticketed you on separate tickets within the same pnr. They could have just booked you as a connection with a DL codeshare flight number on the VS flight and that would have made it Delta's responsibility for the itinerary. Nothing can be done about the BA bit though that has to be a separate ticket. The only reason I can think they didn't do that is it was cheaper for them to issue split tickets and they probably profited from it.