seems as though you can basically do whatever you want in terms of wrist movement, as long as the tip travels in a SLP, and you won't have tailing loops? assuming your hauling at the right time and stuff also.
Lets assume your previous backcast was great and the line is stretched out straight behind exactly horizontally . The objective it to then achieve a straight line tip path that is also perfectly horizontal.
If your line is angled up behind you, and you achieve perfect SLP on your forward cast but it is angled up 5 degrees in front of you, you will likely throw a tailing loop. This is why so many surf casters who fish areas with high beaches behind them use short shooting heads that don't reach the beach behind them on the backcast.
So the objective is for the trajectory of the SLP to be a continuation of the line behind you. Trajectories can be changed easily when false casting short lengths of line by opening the loop, shortening or lengthening your pause, and making pretty radical changes quickly without tails. But your trajectory should be establilshed as soon as possible when distance casting so you can tune your stroke length, haul and turnaround timing to achieve SLP that is in a direct line with your previous backcast.
Most of this is entirely unnecessary for fishing, but I sense a dangerous distance disturbance bouncing around your head, and if it takes root, some of what I'm saying may make sense to you later.