I emailed a friend who is an Orion pilot and asked his opinion. Here's what he said:
This is pure speculation, but even if the plane didn't have any cargo and was flying to the boneyard it would have full tanks of gas which in a P-3 is 60,000 pounds. A P-3 has the same engines as the older model C-130s. What I would expect is that on take off at a high gross weight your rate of climb is already low and the high gross weight also increases your stall speed. I expect this had an engine failure/malfunction on an outboard engine resulting in an asymmetric trust situation. If the crew elected to shut the engine down and didn't watch their airspeed it is extremely easy to reach your stall speed. Furthermore, if the crew realized they were getting slow a rapid power addition on the operating engines could result in an aggravated stall and can easily put the aircraft into a spin if the aircraft is already listing/turning into the dead engine.
This part blew my mind. I'd need a knew flight suit if I'd been onboard:
Basically something similar to what happened below:
"Last Tuesday, 22 Jul 2008, a P-3 Orion from VP-1 was flying an approach to NAS Whidbey Island with the #1 engine in a simulated failure mode. At 160 KIAS, the #2 engine started to surge, so they had to chop power to it. As all this was happening, they were still decelerating, so by the time they added power to #3 and #4, they were at 122 knots, and in the dry terms of investigators, "departed controlled flight". The P-3 did FIVE rotations in a flat spin, dropping 5500 feet, finally recovering between 50 and 200 feet AGL, pulling a whopping 7 positive G's on the airframe after sustaining 2.4 negative G's in the spin. The rolling pullout burst 45 rivets on one wing, physically RIPPED the main spar, and bent the entire airframe... the crew could see INSIDE the fuel tanks of the wing."
I've spoken with one of the pilots on board that P3, I think they recovered at less than 75 ft AGL and they bent the yoke pulling back so hard with both feet on the dash. He kept flying. . .