And to keep the turn tight, rather than increase power this kid decreased power quite significantly.
And you know what... He was most probably right.
In a PPL-style steep turn, which is usually initiated from cruise speed, the objective is not to lose any speed or altitude. Since in a steep turn the g load increases, so does the drag, and to offset this we increase thrust - thus the increase in engine power.
In a tight turn inside a canyon the objective is to decrease the radius. For any given bank angle, the lowest radius can be obtained by flying as slow as possible. So decreasing engine power so the speed decays to just above the stall speed for that bank angle is a good idea.
It is important to realise that this is not the only method of decreasing your radius. You can also maintain speed, up to as high as Va, and roll on the most bank that the aircraft can handle for that speed without getting into an accellerated stall or losing altitude. In a normal category aircraft the smallest radius would either be obtained at Va, with a bank angle of 75 degrees, giving a g load of 3.8, or at 1.4*Vs0, with flaps extended and a bank angle of 60 degrees, giving a g load of 2 - which one it is depends mostly on the difference between Vs0 and Vs1, which is different for each aircraft. And not all aircraft have the engine power to sustain that sort of steep turns, of course.
But I doubt whether you would be able to change your film in such a steep turn and g loading.
To be honest, I think that your pilot had all these things worked out beforehand: Passenger comfort vs. aircraft ability vs. canyon width. You would not be his first passenger for which he had to do a 360 inside that canyon.