Loading/unloading is a legal exemption to the DYLs, but can only take place as long as necessary. So having a cup of tea halfway through or a quick fag, doesn't count. Clearly the car cannot be left open if you're carrying chattels up to a flat, so a CEO is correct to serve a PCN if there's nobody around, but the council should cancel a PCN when receiving representations that show that unloading was in progress. I suggest you add to your existing collateral, (proof of contract starting early last week, and end of tenancy) some photos of the chattels you were engaged in unloading.
Where did you park the car after completion of unloading ? Fit this was some distance away, it emphasises the necessity for parking on the DYLs to unload.