To clarify your setup, you are presenting a loss of visual reference while at low altitude and during acceleration phase, is that correct? it seems to be logical that is your condition that is being looked at..
Correct. We do low visibility runway takeoff training at night. Pilot usually flying from the right seat. I suspect as they are accelerating and rotate to climb attitude, as the runway starts to disappear below them there is an inclination to fly left to maintain visual contact with the runway for as long as possible. When they lose sight of the runway they are already in a left bank, and probably with the somatogravic illusion they instinctively pitch forward. Before you know it they are in a nose down left wing low attitude with 2000 fpm sink rate and punch a hole in the grass next to the runway.
What might have happened in the Bryant accident is similar to what I see in the simulator. The pilot was in sight of the 101 freeway in very marginal weather and he's flown left to maintain the best view of the ground reference (the freeway) from out the pilot side window. He's lost visual contact with the ground, commenced an immediate climb as per IIMC procedure, had an oopsie moment and pitched it forward (incorrectly) sensing the climb attitude was too steep. Sensory overload, nothing computes any more, and the rest is history. The instrument scan and IFR flying skills were not to the required standard for flying in real cloud for the first time. I'm guessing the pilot had never done an IFR recurrent check in the Level D S76 sim. The place to practice is in the sim, punch a few holes in the pretend ground, reset, and try again. Unfortunately in real life the ground is much harder, and there is no reset button.