IMO, 'No loading' is a red herring.
Yes, the sign is still in situ it would appear, but no kerb blips therefore no loading restriction as confirmed by the contravention grounds. A redundant sign is not a defence in this case because it doesn't bear upon the issue which is that the clock was not set correctly - out by at least 2 quarter-hours if not more. Failure to display correctly means that the motorist cannot claim the exemption.
OP, just submit a 'terribly sorry made a mistake in setting the clock' representation. But add something along the lines of..
For future reference, when you received the PCN you didn't immediately notice that it was the clock that was at issue (you had inadvertently set it at 10am) and therefore you looked around for other indicators. You then noticed the 'No loading at any time' sign to the rear of your car - it can just be seen in the CEO's photos. You park in this area regularly and wouldn't want to fall foul of a loading restriction, which you understand prevents waiting by BB holders, therefore for clarity would the authority please confirm if there is a loading restriction in this area and its extent.
Are you the registered keeper with current DVLA details?