If he had told them he was struggling he could have got a SRA approach to 2 miles and wouldn't even need to change to tower to get his landing clearance.
All it would have taken was "Approach PAN PAN PAN xxxxx I am single crew and struggling with work load request SRA approach."
Few swear words in the radar room a second desk opened up multiple phones being grabbed to area telling them to slow things down maybe slots triggered to the regional departures. And something for the next TRUCE exercise.
Be interesting to hear from a ATC persepective what would have happened if he had done this. I certainly wouldn't believe it would have ended up in court.