Can someone explain to me why 300HP applied to a large rotor
at ~700 RPM is enough to lift a 2000lb helicopter straight up,
but the same 300HP applied to a smaller diameter propellor
at ~2600 RPM can not even come close to allowing a 2000 LB
airplane to climb vertically?

Think of the airplane as a boat. Take a 30 foot boat and put in 300 hp
motor and a 6" propellor. It will not move the boat much. But put on a 2
foot prop and low rpm and you will move the boat quite nicely. Air is like
water.

Colin