FR Delay, not cancellation, but it resulted in material loss

Tricky one…

Last flight out of STN on Ryanair was delayed by 2.5 but not the magical 3 hours. If we had taken it, it would have gotten us to our rural destination two hours after our car hire office closed, stranding us at the airport.

Brianair offered rebooking to a flight the following day, but the car hire was pre-pay and non-refundable, we would have been no-shows, so we would have lost that anyway.

We thought we’d get refunds from Cryingair instead, Amex Plat the car hire fee, and rethink the trip. However, Sighingair’s refund page declines the refund, showing us as ‘No Shows’.

Is there a better way to convince the low-cost giant to give us back our cash?

Should we make a full claim to the Amex Plat for everything? Or is our action ‘disinclination to travel’?