I find the instructions opaque. There is no such sign as 'A1 or A1 and A2 Pay and display' in the road and there's no plate on the non-existent payment machine.
But putting this to one side.
You were parked from at least 5.19, not 5.27.
I thought I had booked this and was surprised to get a PCN, but have found that it must not have gone through; signal is notoriously bad on this street and it often takes multiple attempts to get the app to load. I thought I had managed this time but clearly not.
IMO, you do not have a statutory defence based upon your account. The CEO was entitled to issue the PCN because you had not obtained parking rights as required, which you acknowledge.
Whether if you* carried on you could get them to revise their stance, perhaps providing further info from you side to substantiate trying to register, or even elicit a material procedural impropriety in a Notice of Rejection, no one knows. Carrying on to the NTO would involve the full penalty which they could still discount in any NOR, but it's at their discretion.
*- next stage is Notice to Owner to registered keeper. Is this you and are your DVLA details current?