Well this is what I would do for disputes in general. I haven't got past point 2 for a long time.

1) Pursue chargeback.

These are schemes run by the payment processor, visa, mastercard, etc and for the exact rules you want to check with that processor.

I believe for visa you can claim chargeback for tickets for future services up to 540 days from purchase (so you might be able to chargeback the original transaction) as services not delivered. But you should check this - the chargeback t&c’s can be found via a google search and then find the reason applicable for you.

I would tell the merchant (TK in this case) I will file chargeback to give them opportunity to change their mind. Then prepare the supporting evidence needed by the bank (there will be a form).

Once submitted TK would need to mount a defense, and it is the bank/payment processor that acts as judge. Not TK! So the key is to tailor your evidence to show you have a valid claim under the reason code you are applying for a chargeback under.

2) Insurance claim - TK have said they would not refund which should be sufficient for claim but you need to consult your policy to see if such an event is covered.

3) Statutory protections. In the UK The Credit Consumer Act (sect. 75) holds banks jointly liable for items purchased on credit over 100gbp.

Perhaps the DOT would feature here but that is not something I have any knowledge on.

4) Small Claims Court for breach of contract leading to a loss (known as tort). You should research the doctrines behind tort for your jurisdiction. Be thorough and reasonable - your time is valued at a demonstrable rate (perhaps your hourly rate) for example. You should file against the ticket office who issued you the ticket (so if it was the LAX ticket office for example, file the complaint against them). If they are ruled against, and don't pay up, then send in the bailiffs to take their IT equipment and completely down their operations until they suddenly realize they have the money to pay and a massive service disruption isn't worth it...

That should keep you going.

The key is to keep things factual and exclude anything emotional. And keep TK informed of what you are doing and why - in the kind of "if you do A, I will respond this way". That method removes emotion. Give them every chance to change their mind