I'm the author of the Swirl proposal mentioned above that argues for Crossrail 2 to run via Earlsfield, not Balham (or Tooting). The primary reason being that it looks likely to me that Crossrail 2 would make the Northern Line worse, not better. To back this up, I've analysed journey times if Crossrail 2 were in existence at Balham
It is detailed reading, but what it shows is that the saving on journeys like Morden or Tooting Broadway to Victoria or Euston are so small, that most passengers won't change to Crossrail 2. However, the savings for passengers from places like Epsom, Chessington, Kingston, Wimbledon and Raynes Park to the City are significant enough that they will want to change from Crossrail 2 to the Northern Line. Routing the Crossrail via Balham looks like a nightmare for the Northern Line to me.
Relevant to this thread on Wandsworth Common is that so long as Crossrail 2 goes via Balham, there has to be an access shaft between Balham and Clapham Junction. If not Wandsworth Common, then where? As such, another way to save Wandsworth Common is to argue for the Swirl plan
via Earlsfield. Just mention "Crossrail 2 Swirl" in your response to the TfL consultation!