It's weird, I notice that if I just focus on throwing a tight loop on the forward cast, the line goes farther than if I try to power the cast.
That's not weird at all, and it's pretty much the secret to improving your cast. Casting is not about power or strength, but speed and timing. In fact, too much effort defeats us. If you'll remember from your Lefty video, the casting stroke is a gradual, continuous acceleration to a sudden speed-up-and-stop. But, what I think many casters need to hear is speed-up-and-STOP
The first part gets all the line moving with the constant acceleration putting a bend in the rod and storing energy. Then the speed-up-and-stop adds speed to the line and causes it to unroll when the rods stops.
If we add too much force to the cast we cannot stop our hand fast enough and it drifts forward causing the rod to dip down and throw the line in a heap. (An oversimplification, but true enough.) Also, the fastest motion of the rod must come immediately before the sudden stop. Often if we overpower, or try to throw a cast, we accelerate too quickly and reach our fastest speed too soon - say midway through the casting stroke - and the rod actually slows down before the stop. Obviously the rod loses some of its load (stored energy) this way.
I like the trick I've heard of throwing the line at the tip of the rod. Trying to make the flyline hit the tip on each cast has the effect of tightening the loop and teaches better form. It also shows how little effort needs to be used to make good casts. Focus on throwing tight, effortless loops and you'll be amazed how much better you get.