Very interesting discussion, and I appreciate everyone's input (and patience!) as I attempt to make sense of all of this. It's surprising how little of this information is in the current helicopter training manuals.
From this discussion, I would expect that the effects of inflow roll would be much more pronounced on takeoff versus flapback, but I've found the opposite to be true in flying and instructing. In theory, while in a no wind hover, we are experiencing no flapback or inflow roll. We move the cyclic forward to tilt the rotor disc and start our transition to forward flight. We need a little left cyclic pressure and some footwork to keep the nose straight, but somewhere around 20-ish knots, we need a distinct forward push on the cyclic to keep everything where it was going just a moment before. What is it that makes this one moment seem so different than any other phase of flight? Or is it just in my head?