Their letter of refusal is flawed. Whilst a CEO may see no loading activity, it doesn't mean the exemption doesn't apply when the PCN is challenged. The activity of 'loading' includes all the activities necessary, including taking the goods to where they can be accepted, exchanging paperwork etc. During this latter activity, the vehicle may be unattended and locked.
However this is all irrelevant, because loading is barred 24x7 where you parked, and it is clear from their photos that the double kerb blips are visible, (see the photo with the bicycle in it by your car).
The PCN signing aspect is trivial and not something that would win at adjudication. There is no requirement in law for it.
So my view is that whilst you have the absolute right in law to appeal to London Tribunals, you would not win on the above. However, there may be a technical appeal based on council mismanagement of the enforcement process. There have been several cases now where it has been shown that the on-line pages for submitting representations are flawed. I am not an expert in this aspect, so hopefully somebody will come on here and advise.