There are two other initiation techniques you can consider teaching them. One is easier than the other. Both will replace the pivot/heel-push. Both will give them better grip at the bottom of their turns.
The easy one is an "extension turn." It's easy because they are most likely already doing some version of the first part of it. But their version includes a pivot, and the extension turn should not have a pivot. Here's how I teach it.
1. Start on a low pitch, wide slope, with little downhill traffic, at slow speed. Do this progression here until it succeeds, then proceed in increments up to higher pitches and thus higher speeds.
2. Complete all turns once they get to the linked turns part. Heading across the slope is absolutely necessary to give them time to experience and think about what they are doing during the top half of every turn.
3. Step one: traverse, with upper body facing somewhat downhill, uphill hip and foot a bit ahead of downhill hip and foot. Notice that the uphill leg is short because of the hill and downhill leg is long. ..... Lengthen uphill leg. Do nothing else. Then shorten it. Lengthen it, shorten it, lengthen it, shorten it, repeat, in a traverse. The goal is to do this with one leg and not do anything with the other leg, purging the pivot.
**A heel-pusher usually stands tall at the start of the turn to lighten the skis, so they can be pivoted. There should be some familiarity with this movement, but maybe not in the detailed way I'm describing, with only the uphill leg lengthening (extending).
4. Notice that the skis will want to turn to point downhill when that leg lengthens. This is not due to a pivot. There are other forces at work. When that leg shortens, the skis should go back into a traverse, all on their own. Keep it up in both directions, until they are convinced that the skis turn on their own without them doing anything else but lengthening that uphill leg.
5. Now have them do the same thing but allow the skis to point straight downhill. Then shorten that same leg. On a low pitch slope this should be non-intimidating.
6. Now have them do the same thing, allowing the skis to point straight downhill for the length of at least one ski. Both legs will be long; they will be standing tall, with upper body facing downhill. The skis have turned beneath their upper bodies. .... Shorten the other leg, which will become the uphill leg as the skis turn themselves. ***Allow the skis to turn beneath the upper body, so they are again facing somewhat downhill as they go across the slope. This is important. ... They will have just made one complete turn by lengthening one leg, standing tall at the fall line, then shortening the other leg.
7. Now link these. Traverse to traverse, for completed turns. Body facing somewhat downhill the whole time.
8. Move to increasingly higher pitches and you're done. For teen thrills, do this on a slick hard-snow black groomer. Encourage them to count 1-2-3 when the skis point straight downhill, so they don't pivot them out of the schuss. (!!!) Shorten the other leg to get the skis to turn across the hill. The brave will feel very proud.
9. Important part: ask them to verbalize what they've done. Purging the pivot should be a part of what they say. You might, in teacher mode, ask them at every transition from one part of the progression to the next to explain what they just did and why. Verbalizing embeds the mental part of learning.
I've been taught this progression twice by examiners. The most impressive example was in a training session while doing wedge-christies The trainer was a PSIA demo team member (also examiner). I've been this taught while doing parallel turns by an examiner on a very hard double black groomer. Many of the instructors found their bodies unwilling to stay in the fall line and allow the shortening leg to create the turn on its own. They bailed. Some of your teens might consider this fun.