Partly there's a question about the curvature - way too tight for modern "new platform" standards but also if you look on the aerial view you can see that the closed platforms are very short compared to the ones in use. Extending them would mean building out across a bridge and also possibly into land the railway doesn't own. Apparently the platforms were closed during electrification based on the difficulty of extending their length. Even if it were possible to extend them, you'd be encroaching into even tighter curvature and I would imagine it would be hard to argue they weren't "new platforms".
So, I can't see it happening, sadly.
Platforms at Camberwell serving the Denmark Hill trains but not the LJ trains would be ideal: some extra services available at the cost of a bit of an extra walk, without slowing down LJ services with an extra stop