A balanced turn at a safe speed will not cause the load to shift.

Yes, if I understand the narrative so far, these operations are somewhat 'just in time' and 'we need it now' rather than a planned and scheduled flight. How long had the crew been up before launching this mission I wonder? I know the constant drone and vibration of a C130 could put a declared insomniac to sleep in minutes and I imagine a recip like the accident aircraft would have similar sleep inducing powers especially at that time of night on a crew that may have already had a longish day. Just agreeing that maybe they weren't as sharp as they could have been as they made an all too familiar approach. Flaps down?

Back side of the clock although the first leg on this one looks like it should not present a problem. Tag legs after a back side of the clock leg usually involved not 100% capable crews, depending on their rest preparation prior to flight. I flew a lot all night international flights, 3 crew, with adequate preparation and never felt degraded. On those same flights I've seen reserve pilots called out to fill a slot that could/would not use their rest period and were toast at the end of the flight. But, at one of my two airlines, we used to have an easy MIA HAV charter turn around that left at midnight and returned at 2 that was easy peasy. One night we had to wait for 2 or 3 hours to get going back to MIA. We could not get a checklist done right to save us. I think there is an NTSB report of a DC-8 crew who after a long day crashed moving the AC under part 91 with no limit and the conclusion was fatigue.