Connections are the area where BA tends to default to "no compensation" since frankly they rarely spend the time delving into the details, until CEDR forces this to happen. If that 52 minutes was genuinely BA's fault and due to ground staff issues, and that resulted in the missed connection, that that is in the frame for delay compensation. However ATC delays at JFK are endemic as I know very well indeed (and indeed experienced a few days ago) so a lot will revolve around some quite detailed data, which neither of us has seen. CEDR can get those logs published, so if you suspect that there is more to this than ATC then you should consider the CEDR route.