Don't know about trains from Stanstead, the shuttle bus service is pretty good, but there are good, regular trains from the centre of London to Luton.

Have you checked out City Airport at all? They land in the middle of Docklands and have excellent links to the whole of London by car, bus and rail. They also do international flights, but the take off is a little precipitous.... it appears to go up at about 45 degrees or more to avoid the Canary Wharf towers.....

LTS