When going for distance a lot of folks tend to overpower the forward cast and dip the tip of the rod too far. Try for a smooth acceleration, keep the tip up, and haul smoothly and drift your hauling hand up- a sudden jerk, without drifting your hand up can cause shockwaves in the rod tip that ripple into waves in the fly line. More than strength or raw power, it's the smooth application of acceleration and "hard stops" on the forward and back cast that generate line speed. Drifting back a bit after a hard stop on the back cast may also give time for the line to straighten out behind you and help provide a smooth acceleration of power on the forward cast-- starting the forward cast fast and slowing will also cause waves in the fly line because the rod tip will start to bounce as it unloads. Better to start the forward cast a little slower and speed it up, ending with a hard stop, and drifting a bit on the backcast seems to help a lot of folks to do this. And it might be especially helpful with your rod since it probably has a slower "recovery" rate. ( the "recovery" rate is the time it takes for the rod to stop wiggling after you wiggle it. Modern high end graphite rods have a fast recovery transferring the energy to line speed, fiberglass rods tend to keep wiggling a bit transferring less energy to the fly line.) Those "SNAPS" mean you're cracking the whip--- not waiting long enough to let the line straighten out. Remember the more line you have out, the longer you'll have to wait before it straightens. If you have to start the cast too soon because the line is going to hit the water the cast is running out of gas- you have either too much line out for your stroke to carry in the air, are dipping the rod tip, or haven't come to a hard stop. Having someone watch and analyze your stroke is a great idea to give you feedback.
Here are two good links for the double haul- the first shows the basic motion, the second gets into more detail. Notice how smooth the casting stroke and the haul are and how the hauling hand drifts up to the casting hand after the haul.
Just a couple of other things, since you're a little new to fly fishing and using a weight forward line, you'll find that the hauling will work better when you just have the first 30 feet or so outside the tip- this is the thick, heavy head of the fly line the rod is designed for. If you try hauling with more fly line out of the tip you'll run into some problems with the additional weight of more line and the thinner tapered fly line starting to hinge and causing waves in the fly line and the cast will start collapsing a bit. So for instance if you want to cast 60 feet, better to get 30 feet moving fast and shoot an additional 30 feet on the cast than to try and keep 50 feet in the air false casting and hauling to shoot 10. As your casting improves this will be less of an issue and you'll be able to carry more line in the air.
Keep at it, think smoooooth rather than power, and work on the fundamentals. Since you're new to this, you might want to try and get to 60 feet without hauling, just using the basic stroke, and try and hit 60 by reducing the number of false casts starting with 20 feet or so outside the tip. Try not to use the haul as a crutch to hit shorter distances unless the wind is howling. Once you can do this, start then start adding the hauls to get a bit further out.
Oh and keep those trip reports of yours coming!!!