The nothing-at-stake problem can be overcome by GHOST protocol or similar
This is far from clear to me, the obvious formulations of that would seem to have infinite convergence time to me.
You've given a pretty clear explanation of one aspect of the problem though another one with common causes is costless simulation: e.g. some early large number of stake holders can go fork it off and with no cost produce a simulated chain which a new node cannot distinguish from the original. They can do this at any point, even after exiting the system, years later so it doesn't seem possible that any inside-system incentives can prevent them from doing so.
Hmmm. That's a fine example of withdrawing your support from a blockchain (by creating an attack chain) without making the repudiation or withdrawal of support visible on that blockchain (because it hasn't happened yet).
And you're right, the GHOST protocol doesn't address it. Darn.
There are partial protections such as checkpoints in the downloaded wallet, but the most they can do is limit the length of the 'simulation' or attack chain.