You never need to threaten. You just proceed, in order, with your evidence pack attached at every stage. Your Case Manager can draft each of these too.
Cite your deadline. Request the individual decline reason for each numbered claim. Nothing else; each round should be shorter and sharper than the last.
Regulator complaints are quick to file with a prepared evidence pack, and providers answer them differently than they answer you.
Through your bank, with the evidence pack attached. A documented, numbered case built on the provider's own records is exactly what chargeback review teams want to see. It is what the pack was built for.