Agree all of that, bookworm (you'll not be surprised to hear). There's another bit - the blade angle of the propeller.
Depending on the pitch of the prop, it may produce relatively little "pull" when stationary relative to the airflow, and a lot more as it reaches optimum. So you may find you get better acceleration from the prop as you approach Vr. Variable pitch props help a lot here!
However, aerodynamic drag being proportional to the square of the airspeed, it's not likely that the blade angle will help if you aren't past 75% Vr by 50% runway.
I did the sums for Chateau La Chassagne, and concluded we'd still be on the ground at the far end if I tried to take off at MTWA. So we were light: 2 up, not much baggage, and 2 hours' fuel (no reserves) and aimed for 80% Vr by 50% runway.
I didn't get to check - we were airborne by the 50% runway marker. Weight makes a big difference.