ParkingEye - Parc Llandudno - 2 hour free parking then Pay and Display

My wife visited the site and stayed for a total of 3 hours 7 minutes. She paid cash for additional parking time at the pay and display machine. Ticket has since gone and we don't have our own paper trail. She insists that she had to put the reg no. in when paying, which makes sense as they use ANPR cameras. I've appealed the ticket and they have asked for proof which I don't have. Can I ask them to supply list of reg numbers punched in around time of when my wife purchased her ticket? Only explanation I can think of is her putting a wrong digit in. Or is there a better way of tackling this issue?

You can appeal on the basis of a potential "keying error" (see https://www.britishparking.co.uk/write/Documents/AOS/Sector%20Code%20Templates/sectorsingleCodeofPracticeVersion1.1130426-2.pdf )and give them as many details as they can, and they may check their records and agree to a payment of £20 as a full settlement if they find the mistake.
But be clear about how much additional time was paid for, you are not. If an additional hour was paid for, the "grace period" of 10 minutes should cover the extra 7 minutes, for example.