I don’t really have an answer but why would you even want two running agents using the same socket file path, one with an unlinked socket and one with a socket actually existing in the filesystem? I assume you want to avoid a gap between stopping the old and starting the new agent?
My next step would probably be to check the openssh source code for the bit that removes the socket file to see what kind of conditions there are and maybe also try strace or similar tools to see if it does not remove it because the removal fails or because it is never attempted.