[Symph]

Ether, I am sorry to say that we are both unfortunately confused. You see, I had redone the math and was going through the process of updating my post in stages; Replacing my "MathProofCondensed.docx" attachment, replacing the graph for my trajectory in the original post and finally responding to you, when my Wi-Fi cut out for a full day. Which I thought was fine, considering that I had finished updating, until I realized that I had neglected to explain why I still went for 39 degrees even with an alternate velocity, and left my original sentence "Well, for us, it’s 39 degrees at 42.5 feet per second." unchanged.
I will first begin by explaining that I chose 39 over 36 degrees knowing full well that it would result in an Rs of 11.5ft rather than a full 162in or 13.5ft, because although 36 degrees does give us the greatest strip of the field, it's furthest point lies in the middle zone rather than the beginning of the first, where we will not be shooting from leaving a potion of that strip wasted, and it's closest point is several feet away from the goalie zone, forcing us to shoot from further away and over build our robot.
If you graph the function "R''s=-115.7137 *csc(⁡a)*cot(⁡a)" in my proof, you will see that one of it's many zeros is in indeed ~36 degrees, and does indeed, as you calculated, result in Rs= 13.5ft.
As you can see now, my math is right, but my final decision does not match what I first defined as "optimal", and so in the name of peace, harmony and all things good in the world, I am going to update my post, once more, this time sticking to my original postulate of "best angle and velocity => biggest Rs".
Hopefully this time, I will have it right,
Wish me luck Ether!