If you could edit the beginning where you show the percentage 40,100009% (needs a decimal) , my OCD would feel better. Otherwise this is an excellent explanation.
You've done the maths incorrectly, or focused on the wrong numbers in figuring out the efficiency.. Let's take the numbers you gave (very roughly). Easiest way to see this is to suppose the sender has "just enough" to complete the volley to about 1.8b. He "makes" about 300, so he had to start with 1.5b to complete the volley. After the drop, you're left with about 1.1b, so you've lost 400m. As you stated the receiver gains about 300m. The efficiency isn't decided by how high you volleyed up the ally. The highest total value the ally reaches before you drop is completely irrelevant to calculating the loss incurred (or the exact amount you lose by dropping from it's value @~40% of that). All that matters is how much the receiver got and how little the sender lost. And that efficiency is about 75% (300/400). As the OP correctly notes, after about 50 volleys, the efficiency doesn't change much. 75% is about as high as you can get.
I like it even though it's old it's pretty detailed. Color is good way to highlight the points. I give it a 7.5 maybe 8 out of 10.
I think the game uses exactly 1.5% and 40%. The reason you got slightly different figures is because at every stage the gold is rounded to a whole number.