My credit card company investigated the issue with Visa, and eventually they charged back the full amount of the transaction. It took several months of investigation and I had to provide a lot of evidence such as:
- Screenshots, which luckily I took at the time of booking, showing timestamps of when the booking was made
- Emails from TAP confirming I had cancelled the booking and requested a refund
- Info on the 24h policy and proof that TAP was refusing to honour it etc.

TAP made a lot of claims that weren't true, and I provided all this to my credit card issuer to help with the investigation, showing that they were making conflicting claims (such as saying I actually cancelled it after two days, or that I had requested a voucher, or that the policy doesn't apply).

I never even heard back from the DOT (even a year later, nothing).

Glad I got it finally sorted and I got my 600 euros back. I'll never ever deal with TAP again, the scumbag liars.