Airbus produce some very nice apps for loadsheet and takeoff performance for use on an EFB, as part of their Flysmart package.
The loadsheet app can be used with simple inputs such as males, females etc , which bays they are sitting in and where the bags are. The app requires a specific reg as a basis to start computation. The app then produces a loadsheet and the data can be inputed into the take off performance app.
When I have been faced with similar problems I have asked the dispatcher and crew to make simple counts and then used the apps, normally the data would come from the DCS.
BA I believe send an acars message to the aircraft with the loadsheet data and aircraft performance figures.