Pete: Thanks for answering my questions. You have painted a much beter picture now. I'm happy to give you some thoughts, but my overall concern is that this thread has become voluminous with so many suggestions that we all might overwhelm your focus. So here are my 2- cents. Unfortunately this may put you to sleep by its finish.
First, defining the "cross-over turn" mechanic. It is when the center of mass crosses over the center of the ski as weight transfers from one set of edges to the opposing edges during turn initiation. It occurs typically in medium and larger radius turns. The "cross-under turn" mechanic is when the skis move under the center of mass, and then away from the CM, while it remains in a relatively single location, during turn initiation. The skis travel in one direction away from the CM and then return crossing under the CM as they move in the opposite direction.
With regard to your alignment correction. Did the boot fitter also make any changes to your fore / aft alignment also known as "ramp angle"? I ask this only because you made a statement that your skis "rebound and get away from you frequently". I assume they have also corrected for any ramp angle problems. One last item here. Are you wearing stiff (race type), boots or more contemporary softer all mountain boots? Stiff boots will frequently push a skier into the back seat syndrom, which causes the skier to make other body mechanic adjustments in their turn mechanics to correct for this problem.
My question on in-line skating, was with regard to how you move your body parts in a turn while skating, not about tricks in a skate park. For instance, can you make slalom type turns on in-line skates with your arms crossed across your chest, the same way we do on skis (assuming you have seen this done on skis)? In so doing do you turn without over rotating the turn finish on skates or are you set up properly for the next turn? You should be able to tip the in-line skates and turn without much foot steering and still not over rotate the turn.
My question on turn initiation. When you initiate a large radius turn you mentioned that you move your body across the skis, but when you initiate short radius turns you "roll my knees". This leads me to believe that you are doing both a cross-over movement and a cross-under movement in each turn actively and correctly for the turn size at the time. My only thought here is that you may have a lingering hip rotation in the short radius turns, which you wouldn't notice in the larger turns, due to the speed and change of direction being only slight in comparison, therefore not causing any noticeable slippage.When you move to the short radius turn on hard or icy surface conditions you will find slippage if there is any hip or other upper body rotational forces in your turn mechanics. You will not be able to see this rotation in your video either in larger radius turns, but it will show up as an abstem (downstem-outside ski moves away from the inside ski), typically at the end of the turn when the centrifugal forces are at their peak. If you do observe this in your video your clearly twisting your skis under you not tipping them to initiate the turn. You also mentioned that you tend to "bank a bit on turns to the right". When this happens do you find that the short radius turns to the right end with washing out (slipping), the left or outside ski? Does this happen more frequently in the right turn and are you aware of more weight ending up on the inside ski (in this case the right ski), as opposed to when you make short turns to the left? If this is what is happening then some skiing fundamentals need to be mastered to correct and change these current movement patterns.
Lastly you mentioned that you "go from a high edge angle to another high edge angle surprising the ski". This is clearly a pressure management problem. Some of the other folks, I believe it was Ott Gang, that focused on this made it very clear that an abrupt edge engagement would cause the skis to slide on the hard surface. I fully agree with Ott. We ski alot of hard boiler plate conditions back east here and find that pressure management is critical if we're to be successful on this condition. Ice or hard pack always points up our flaws in technique, due to the precision needed to ski it successfully.
Now for a few last suggestions and a mini short-turn progression with some related tasks.
First I would like you to rebuild independence in turning each foot / ski independently from the other. Do this by practicing some sideslipping straight down the fall line in each direction until its second nature. Do it in all but powder conditions.
Next add to the sideslip a linking of one sideslip to another in each direction at the middle of the practice segment by releasing the skis edges and twisting your skiis under you a full 180 degrees, so they face in the other direction and then continue sideslipping. Do this until its easy and can be done on command. Here's a hint. Keep your stance open (feet apart), throughout the exercise.
Next do hockey slides to both sides straight down the fall line until it is easy. Hint-Don't go fast. Do all of these exercises slowly.
Now link the hockey slides without using a pole touch yet. This will change these to pivot slips. Hint- Keep your feet and stance open even more than you did earlier throughout the exercises. Additionally be sure to extend your center of mass to be ahead of your feet / skis as you do this or it won't work. Specifically, your hips must lead your feet / skis and be kept up or you won't be able to turn your feet independently. Your feet should feel like you're on a ball bearing surface.
Now add a pole touch for enhanced timing. This IS NOT a blocking pole touch. It's a light touch.
Now add to this sequence some mild and Progressive edge engagement as you finish each pivot slip. Be very light here also. Once this gets a little easier then add some foot steering as you finish the pivot slip, so that you continue turning the skis actively throughout the turn.
Now after you're very comfortable with all of the above add more edge engagement to this sequence (a higher edge angle). But whatever you do Don't rush it or you will defeat all that you have just mastered.
Finally, take this to some groomed green or low blue terrain to practice. NOw go back to the medium radius turns and ski them very slowly all the while tightening the radius of every third or fourth turn until you have begun to ease into short radius turns. Keep your speed very slow now and change from the cross-over movement to the cross-under movement and you're on your way to short radius turns.
Last but not least. If I haven't put you all to sleep yet-Take this out on hard pack to practice until your confidence builds. Be sure not to ramp up the intensity and pace at all until the movements have become second nature at every point. This may actually take you an entire season or two to clearly recognize what is happening in your skiing. Good luck with your practice and I hope I haven't confused you more than before.