Pardon the reply 4 plus years later, but I have recently revised my article on the "NYS&O", New York, Susquehanna & Ontario, which was originally published by the M&NJ RHS in volume 3 #1 & 2, and which has now just been posted on the O&W RHS website. The article deals with the "cooperation" between the NYS&W and the NYO&W as the NYS&W sought to break free of the Erie. At one point the two roads considered a joint operation under the banner of the NYS&O with the M&U as the connecting link. For about 15 months, starting around Dec. 30, 1939, the NYO&W shipped as many as 60 carloads of anthracite daily to the M&U which interchanged them to the NYS&W at Hanford (M&U Jct.). This traffic suddenly ceased on 3/22/41 when it was rerouted via Cornwall and the West Shore RR to Little Ferry and interchange to the NYS&W (thus cutting the M&U out).
Since the engine assignment sheet is dated 2/28/41, it is in the period of the heavy coal traffic via Hanford. So, I suspect that the M&U PD (Per Diem) was NYS&W's daily attempt to forward the coal hoppers back to the M&U by midnight to avoid having to pay the car hire. There would not have been a big need to run this train in other eras as it would not have been justified by the relatively low volume of the M&U interchange. Similarly, I suspect the Coal Job may not be a job to work Edgewater Dumper but perhaps the job to haul the coal from Hanford Jct. to Little Ferry/Edgewater.
Just my thoughts on the matter, nothing you can take to the bank without further documentation.