Bob, I personally do the same thing that Lefty does with forming loops in my hand. I think stripping baskets could have their place in saltwater fishing or something like that, but is a pain when it comes to most other forms of flyfishing. It is a difficult thing to get used to if you are new to flycasting because it requires that you are doing several things at once. The thing with holding loops is you are going to have to shoot your line/load your rod at the same exact moment you are letting the line out of your hand, otherwise like you said it becomes a mess. It is all about the timing with flycasting. It is a tough thing to explain on how to accomplish this in writing.
As good as a video is it can only teach you so much. I was a guide for many years and I saw many people that tried to teach themselves how to cast, often they had a pile of bad habits that are really difficult to break. I would go into a local flyshop if you have one and have them give you a few pointers, and if they teach a casting class I would recommend signing up for sure. It might click a little more if you see it in person or have someone point out what you might be doing wrong.
Unfortunetly there isn't a shortcut in great flycasting, and to become a great caster demands many many hours on the water and lots of attention to refining your cast with help from those that cast well. Don't get frustrated though, remember that great casters like Lefty have spent countless hours working to cast that well and it will take you time too, don't expect to cast like Lefty overnight. We all started at the same point and anyone can become a great caster if they aren't complacent and are willing to put the time in. Good luck!