Well, it's all speculation, but the pilots could have realized at the last second they were running out of pavement and rotated, and the plane have enough momentum to "bunny hop" into the air before stalling and dropping again. If they only made it a half mile, at takeoff speed they'd cover that distance in 15-20 seconds or less. Fully loaded, they'd have no chance to get it off the ground in 3500 feet and keep it in the air.
It probably hit something at a fairly flat angle or in a slight descent (tail low), it wouldn't have had the time or the room to drop the nose a whole lot, I'd imagine. If it crashed in a field, though, and didn't plow through a lot of trees, I'm somewhat surprised there weren't more survivors, even with a massive postcrash fire.
I believe you have the scenario correct.
I am also curious with regard to the passengers being able to escape.
I can only imagine a scenario where the impact jammed all four doors on the plane, trapping everyone.