Thanks a lot for this summary.
I had once heard a talk by E. Mayr, a collaborator of Vafa, in which he summarized some aspects of the stuff related to the topological string that you mentioned. I will have to sit down and look at these things in more detail.
One further question, though:
I had asked Mayr about the role played by Matrix Models in these approaches and I recall that he pointed to a distinction between new, very new, old and very old Matrix Models. I think he said that the very new ones are essentially the same as the very old ones!
All this pretty much confused me, because apparanetly I don't know all flavors of Matrix Models. What I know and understand is the BFSS model and the IIB (IKKT) model.
What other Matrix Models are there and how are they related to BFSS and IKKT?