Averageskier, while "they" say you can’t, I say you can. Given the obvious stance corrections and renewed focus on a forward pole plant, they do not instill dominant motor patterns. If you do in fact happen to be an average skier (terminal intermediate) but also sporting at least an average level of athleticism with average skier's age of say 30's-40"s, you can be taught the complete basic maneuver through an easy set of progression steps completed in only one session. If you can hop your skis at least 6” off the snow keeping skis relatively flat, then you are all set to learn this and many other drills with similar modified progression steps. Learning it can make any intermediate skier a much better skier in general and improving many aspects other than just the bumps. It is simply a leverage move to get your CoM forward thus allowing it to shift back and forth without any of the trouble you are experiencing. If you are not minimally athletic or coordinated or are a true beginner then the drill is not for you.
The dolphin turn is a movement amplification drill from which a resonating movement pattern on an individual’s regular technique will result. I am confident that the difficulty level of the dolphin turn is more a factor of general athletic coordination, strength and agility rather than ski ability. It may not often be used because it cannot be demonstrated by many coaches and instructors who have passed beyond the athletic “window”. While there may be no answer for immediate, on the fly, fore/aft correction on steeps, a new and dominant movement pattern to avoid this from happening will likely be the answer.
Learning to do it with more control, more consistency, longer durations and higher amplitudes can take a full season or more if you were to follow through adequately enough. Along with varying sets of drills, this is the type of season-long self managed learning process that, while somewhat onerous, will provide you, IMO, your fastest rate of development. Self learning is much easier now with a multitude of resources on the internet and video capabilities for mobile movement analysis that can reduce conventional ski instruction costs dramatically.
The original video I posted painted this drill as too advanced and too specialized. It’s not just for bumps but also the steeps you are having trouble with. Video below showing one of the easy progression steps using ski poles and without sliding that you can probably perform at a minimum on your first couple of tries: