What should I do? Condor threatening to send me to collections for a flight I've already paid for (and accounting department customer service hanging up on me when I try to resolve)

In January of this year I booked a Condor flight for travel from Seattle to Frankfurt this summer. They double charged me. Condor claimed they did not double charge me. My credit card cancelled one of the charges and the other payment went through.

In February they sent me an email saying I owed them money (an amount similar to but not exactly equal to the price of the flight). In April they again sent me this email, but saying I owed a different amount (slightly less than they had I owed in February).

Emailing them has gone nowhere, they just say to send them the money and don't respond to questions for clarification.

Calling them has also gone nowhere. Customer service say they can see that I've paid and that they're not sure what the other charge is for and that I'll need to talk to accounting. Their accounting office is only available from midnight to 7am my time. Several times I've gotten up early to call them and either been left on hold for almost an hour, or immediately hung up on, or they talk to me briefly before hanging up on me. In my latest call, the most I've been able to talk with someone from accounting, they said my flight had been paid for. When I asked why I was getting the emails saying that I owe money and that they were going to send me to collections, they hung up on me.

Has anyone resolved an issue like this with Condor? I'm afraid that they will send me to collections and I'm afraid they won't let me on my flight in June. I really don't want this to wreck my credit score or prevent me from attending a family reunion!

I'm not sure what to do next given that getting up at 5am to call Condor to try to reach accounting hasn't been working. I'd really appreciate any insight!