For one, in level flight the planes don't need very much thrust to fly. Given the size of the props etc. most of the prop either is flying at a negative angle of attack and producing very little lift(thrust) or large portions of the blade are both above and below optimum pitch and are mostly producing just drag. It sounds like that in level flight only the center of the prop is producing thrust and the tips are just along for the ride. Then in maneuvers the area producing most of the thrust moves out towards the tips. That would explain using the tip pitch to adjust or combat accelerating out of a maneuver that people talk about. It also agrees with what the racing folks do. They usually use progressive pitch, with the tips at a higher pitch than the center in order to get maximum thrust and speed.
Prop contribution to line tension- it seems counterintuitive, but larger props do seem to help with line tension. One mechanism would be the fact that the aerodynamic center of the plane is outboard of the thrustline, usually in the range of .4-6 in. In level flight there is a moment between the thrust and the drag that would try to rotate the plane out of the circle and pull on the lines. When you go into a maneuver the drag on the plane increases, but the drag on the lines goes down, so the moment becomes relatively larger and the line pull would not go down as much as expected from the slower maneuver speed.
A larger prop, or a three bladed prop, generally interacts with more mass of air, but at a lower acceleration to generate the thrust needed, compared to a small prop running much faster. The greater mass of air moving, relative to the mass of the plane, would give the whole system more inertia and make it respond with smaller speed changes.