Try skiing with most, but not all of your weight set on one ski (e.g. 80-20/90-10/95-5/99-1 - but keeping the same weight no matter which way your turning. From there, White Pass turns (lifting the old inside ski as the turn finishes, changing edges only the new inside ski then start lifting that ski off the snow after passing through the fall line) ought to be easier. After that, traditional one ski lifted all the time (or off) drills become easier.
Most of the one ski drills focus on the transition versus the situation you describe, but any of these drills that teach an unnatural weight distribution can help improve emergency weight transfer situations. With all one ski drills, you can get your weight to the inside by cheating (e.g. tilting, pivoting) or you can do it by moving your CM across the ski. If you cheat, it won't feel easy. If you don't cheat, the drill is very easy. If you don't know how to move your CM across the ski, one ski drills won't teach you how.
Things that will help:
- make sure to finish turns into a countered position
- continue to flex and extend the lifted leg
- make sure the lifted ski is either level or tip down
- don't lift the ski too high, more is not better
- if you can only turn by leaning into it or throwing a pole plant to pivot around, then stop, put the other ski on the ground and slowly back away (from the drill).