I cannot seem to find the appeal that I wrote. I made my appeal for them to see some sense - this has worked in the past in other situations, but clearly in this case I should have been more exacting. I am reasonable sure you are correct that the blue badge being displayed by the driver is not directly impactful but might count towards a mitigating circumstance, especially given the driver was only parked for 4 seconds over the time limit (30 minutes free parking, parked for 30:04).
I am unsure on the grace period - I believe the guideline states that it is not required for short stay parking spaces (<30 minutes), but again the driver being parked for 4 seconds over that time, and having their reverse light on at that time (suggesting they are in fact not parked but driving) is somewhat egregious.