Of course not, because you can actually measure the height of the tree to check against your trigonometric calculation...you can't actually measure energy moving in two directions because it doesn't happen...energy movement is a one way gross flow from warm to cool.
The S-B equations calculate the power from one object and subtract it from the other, resulting in net power going from the warmer object to the cooler one.
Mathematically true, and based in reality. For your version to work then the average temperature of the two objects would have to be able get inside of individual particles and change the internal conditions to block radiation. What is the mechanism by which the movement of molecules is stopped or slowed? Even though the temperature is maintained? Temperature IS the movement of molecules. You make no sense at all.