Yikes, I'm so sorry! Similar experience with us a few years ago. Missus employed same tactics as you; kind, patient, polite, firm, demanding, harsh. Nada. After the third of forth time where she to recount the entire story because "there doesn't seem to be anything in notes on the account", I snapped.
I took the phone and asked if they worked at the local hub or in India. Assuring me they were local, I asked for the address of their centre. "But it's only a call centre, not a service centre. There's nothing we can do here for you." He said.
"That's fine. I'm not coming for service. I coming to burn the fucking building to the ground. You're upsetting my wife and that's ruining my life."
Click.
new upgrades, adjusted billing and a very nice lady making very long apologies.
just a thought.