I’m going to try to challenge the double yellow line along the dropping kerb on the grounds that it does not lead to an access point.
Please tell me you haven't done that!
You cannot challenge the merits of a restriction by means of a penalty charge notice, the merits of a traffic order can only be challenged in the High Court under the procedure described in
Part 6 of Schedule 9 to the Road Traffic Regulation Act 1984, and the time limit for that has long-since passed.
You absolutely cannot succeed on an argument that the waiting restriction should not be there, such a contention is not arguable as a matter of law and the Traffic Penalty Tribunal cannot entertain the argument.
I might also mention that I found myself very stressed and overwhelmed as I had no idea of the mess that was going on in the area (temporary traffic signs, road closures…), to the point that I decided it was better to drop the car as soon as possible as I did not feel comfortable driving there.
That doesn't really add up, if you were so stressed out being there why wouldn't you drive out and park on the next street?
Surely it was not the best place to park, but I thought it was better there than parking on the empty bay, as I would have ended up in the same situation as plenty of space would have been required for the metallic door to do not clash to the car if opened.
The empty bay did not appear to be suspended so you could have parked there, odds are the metal gate opens inwards anyway. Regardless, nothing you mentioned entitled you to park on double yellow lines.
Furthermore, shouldn’t the council take the appropriate measures to remove double yellow lines when they don’t serve its purpose anymore?
Maybe, but it's not something that you can challenge as part of the process of appealing a penalty charge. Really this is a political issue you'd need to take up with the local councillors, who you can find here:
https://www.writetothem.com/It's also not at all clear that the lines serve no purpose, if this is a controlled parking zone then the council is legally required to mark every length of road, there cannot be any unmarked stretches.
Do you have any mitigating circumstances that are unrelated to the parking contravention? Anything such as recent bereavement, financial difficulties, health problems etc?