I don't think it is quite as much in your favour as you think, sorry to have to say it. Having got out of your car, your girlfriend could have had a quick look at the sign, then rushed back to tell you "we can't park here", and you could have driven off, and would have had a cast-iron defense if you got a PCN, because the sign could not be read on approach.
So submit reps by all means, based on your narrative, but don't expect them to respond favourably.