White City platform allocation

It should be remembered that when the extension westwards from Wood Lane opened in 1920, trains continued to call at the expanded Wood Lane station. White City station opened with the North Acton - West Ruislip extension in 1947; it would have provided a less cramped layout than Wood Lane for the additional services to & from the new line and a better arrangement for terminating trains (no moveable platform for a start!)
The flyover for restoring left-hand running predates White City; it would have been the best location for it, a relatively straight section and well away from the stations either side and from sharp curves.

Just north east of White City station was the United Dairies' "Wood Lane" milk depot. Milk trains arrived there for years, and it was served by both the WLL and the GWR link, running parallel to the Central Line all the way to the GWR's NNML at North Acton where the GWR built a junction. This latter GWR line was there and visible although unused until about 1970(ish). Until fairly recent years the milk depot could still be seen under the motorway bridge.

I am not aware that there was ever a link from the GWR to the Central Line there or at North Acton

The E&SB was a GWR project: originally to go to a new (GWR) terminus at Shepherds Bush, with interchange onto the CLR, it was changed to have a link from the CLR at Wood Lane, with CLR having running powers through to Ealing - this is how it was built. Originally there was just one pair of tracks for both CL & GW trains, with connections to the rest of the GWR at Ealing Broadway and North Acton; while from 'Wood Lane Junction' - where the Central Line tracks reverse position, the flyover was part of the junction arrangement - east there were seperate tracks to Woood Lane CLR, and to Viaduct Junction on the WLR. A seperate pair of tracks was later (late 1930s IIRC) built for GWR use between North Acton and Wood Lane Junction, and the various connctions taken out (though it all remained GWR owned until 1948).