Duplicate carry on charge

I’m wondering if anyone has actually managed to get a refund from Flair after being charged twice for a carry-on.
I was flying from Calgary to Toronto and purchased my carry-on online the day before my flight. I have the receipt, proof of purchase, and the carry-on was even shown as included on my booking after I paid.
When I got to the gate, the agent insisted I hadn’t paid for a carry-on. They were extremely rude and kept telling me to prove it. I showed them the receipt and all the evidence, but they still claimed they couldn’t find it in their system and forced me to pay again if I wanted to board.
The agent’s attitude was “I don’t care. If you don’t like it, contact customer service.”
So I contacted customer service immediately. They still refused to refund the second charge.
Their reason? They claimed my bag exceeded the size limit. The funny part is my bag was never measured or weighed, and it absolutely did not exceed the size or weight limits. They simply made that up as a reason to deny the refund.
What I don’t understand is how they can admit I purchased the carry-on (it’s literally on the receipt they sent me) but still refuse to refund the duplicate charge because of an unrelated excuse.
I’m still fighting this. Has anyone here actually won a dispute with Flair and gotten their money back? Is it worth continuing to push, or am I just wasting my time?