Sorry, this is wrong. It has nothing to do with RPM.
You are right. I got axial speed mixed up with RPM
The actual airspeed achieved is the important figure. The theoretical thrust of a prop at a certain airspeed is insignificant if the aircraft never reaches that speed. You could have a model that is draggy enough that a high pitch prop will cause it to fly slower. Not only that, take off performance would be miserable.
Its not the airspeed of the plane, its the increased airspeed of the air going through the prop
It all depends on how much drag the model exhibits, desired airspeed, and available power. You won't make a DR-1 fly any faster or more efficiently by putting a square prop on it, unless you can reduce the RPM to allow a larger diameter at the same HP input. This is what BLW is eluding to.
Nothing wrong here. Except the prop efficiency is the thrust time increased propeller airblast divided by horsepower. If the engine on that DR-1 is red lined and has more power left, then increasing the pitch will increase thrust, and prop speed, and will go faster, though probably by a very small amount. The prop will have a higher efficiency because it will have higher thrust. As for my model a larger prop makes it climb worse and fly slower, though this is because the engine cannot turn it as fast. A smaller prop with more pitch will make it fly faster but climb slightly worse using about the same engine power, however it should be more efficient though less effective.