Genuine question, Not being a jerk, actually think your grasp of the maths is pretty good so I'm curious if you have the answer (which I don't)
Does your method account for the velocity of the hands moving in the opposite direction? I.e. If the hands move faster backwards than the player moves forwards it would reduce how acute the angle would need to be? Or is this not a factor that needs to be considered?
The initial velocity of the ball, other than from running (the "speed" of the pass), is all I considered. I can't think of how that could be generated other than by moving the hands.
It is true that the angle could be smaller if the ball is thrown harder. I don't know what the practical limit to pass speed from either a throwing or catching perspective is, but I've taken a ball going at 10 m/s (fastest sprint speeds) or about 36 km/h.
This is roughly close to the speed I see the ball being thrown in general play, but it is certainly thrown harder sometimes. So that is a 4th possible "compensation", but I assume at about 10 m/s the ball is generally thrown close to it's practical fastest if the pass is to be accurate and a catch is to be made.