There seems to be little information about how Abbey Wood station is going to work. All I can find is that track will need to be realigned but does this mean that Crossrail will use the existing platforms? How will this affect the running of Southeastern services? surely stations east of Abbey Wood (Belvedere and Erith) will end up with very poor service because very few trains will be able to run up the track due to Crossrail trains?
A mile or two west of the station the north track (eastbound) is going to be diverted north, running across the top of the Crossrail tunnel portal. The Crossrail tracks will thus emerge between the two Southeastern tracks, providing cross platform interchange as in the diagram linked above. I believe there'll be a pair of reversing sidings east of the station, which aren't shown on that diagram.
In short, Southeastern and Crossrail services will be entirely segregated. This diagram shows the full proposed track layout.