Making use of overground tracks would do little to improve capacity on the rail network. I would far prefer the same technique as planned in Crossrail 1 and Crossrail 2 - an entirely new tunnel going as far as possible, preferably connecting with existing transport hubs across South London as well as areas with no existing rail network. This might be a route via New Cross Gate and Lewisham or it might be a route via Denmark Hill and Honor Oak/Forest Hill. Alternatively if the Crystal Palace is to become a major cultural destination, then it would make sense to take the Bakerloo line there (underground).

Extending the East London Line from New Cross to Lewisham and beyond makes some sense as it would only be four trains per hour, so it might not impact capacity on other overland routes.