At the risk of opening up a huge can of worms, I have 2 questions and
one statement:

1. If a helicopter makes lift by displacing air downward with its
rotor:

Rotor blades are airfoil shaped (I've seen 'em) just like airplane
wings. Therefore airplanes fly by displacing air downward with their
wings? There's something wrong with your logic Sir Maxim. It would
seem that we killed this theory about 104 years ago with Will & Orv's
little wind tunnel. Recall, the flat inclined surface displaced more
air than any of the airfoil surfaces as measured by the vane balance.
However, it also made less lift than any of the airfoil surfaces at a
similar AOA. Ergo, an airfoil makes lift not by displacing air
downward, but by producing a condition where the air flowing across its
upper surface travels faster, and therefore has less pressure, than the
air flowing under its lower surface. Therefore, an airfoil wing does
not "fly" by displacing air downward, but rather exploits a zone of
differential pressure caused by a difference in the speed of the
airflow. And since a helicopter rotor blade is a long skinny wing
flying around in a circle, it produces lift just the same as an
airplane's wing does. I can only think of 2 machines that fly by
displacing air downward. Those would be ballistic rockets/missles, and
the Harrier jet in vertical or hovering flight.

2. A helicopter glides forward on an inclined cushion of displaced air:

A helicopter flies in a chosen direction due to the cyclic change in
rotor blade pitch impatred by an inclined swash plate. What's a swash
plate do? Well, imagine a doughnut smashed between 2 dinner plates. The
dinner plates are fixed to the fuselage and do not rotate. The doughnut
rotates at the same rate as the rotor head. When you tilt the dinner
plates, you also tilt the doughnut. Now if the doughnut is attached to
the rotor blade pitch-control horns by rotor blade pitch-change links,
the links will go up and down relative to the fuselage as the tilted
doughnut spins. This pushes and pulls on the rotor-blade control horns,
constantly changing the pitch of the blade as it flys around in a
circle. If you tilt the dinner plates forward, the blade flys at a
lower AOA in the front 1/2 of the rotor disk than it does at the back
1/2. Since its producing more lift in the back 1/2 than in the front
1/2, the blade flies higher in back. Stay with me here. As the blade
flies higher, its coning angle relative to the rotor head increases to
a greater angle than it does in the forward 1/2 of the rotor disk..
Therefore, its line of thrust relative to the fuselage is not vertical,
but is actually inclined forward. A helicopter "pulls" itself forward
through the air, more or less.

3. Rotor blades turning at 700 rpm vs. a prop turning at 2600 rpm.

Well, helicopter rotors don't turn that fast. Most are somewhere in the
300-350 rpm range. A Boeing Vertol CH-47's rotors only turn at 255 rpm,
or so I've heard. If I'm not mistaken, Hughes once built some kinda
giant tip-thrust powered test-freak that had a rotor speed of about 16
rpm. I've seen the videos, but I can't recall the name.

I could of course be completely and totally wrong about all of this. It
might just be fairies and Leprachauns.

Harry