We agreed to disagree.
A fly line has both Momentum and KE, but I still believe it is KE and not momentum that determines casting distance and is the reason that a double haul can increase the distance of a cast much greater than the change in momentum would predict.
My point is that if you have two bullets with identical shapes so aerodynamic drag is identical, but one bullet is twice as dense as the the other, so bullet A has a mass of 1M and the heavier bullet B a mass of 2M; and bullet A travels twice as fast (2V) as bullet B (1V), they have identical momentum 2MV. But the lighter bullet A has twice the kinetic energy (4MVV) as bullet B (2MVV).
Which bullet goes farther when shot at the same trajectory? If momentum determined distance, both bullets would go the same distance. I believe that the faster bullet will go farther because it can travel farther before gravity causes both bullets to hit the ground. Theoretically they will hit the ground at the same time.
Similarly, I believe that KE determines the distance of a fly cast. When everything else is the same, increasing the velocity will increase the casting distance. Under perfect conditions, momentum predicts the increase will be linear and KE predicts it will increase by the square effect.
Go out and cast to see which prediction conforms to reality.