As it stands, I will be asking for a full, independent report as to the state of the engine
Given that the purpose of the oil is, basically, to lubricate the bearings are you expecting them to completely tear your engine down to check them for damage?
You say you did a short trip home after the service, but you also say that the cars done 17 miles since the service…. Is this the short trip?
Get them to see why the sump plug came out (they may have tried to fit one from another car or the sump threads may be damaged), fill up with oil and learn from your mistake of going to AC in the first place!