It's probably flattening faster than you want because of the small extension of the inside leg.
Max, seems like you are right. I've been working on SP without extension and the problem is gone, I have no video but I feel it and checked by looking down at my legs and can confirm the problem has gone.
I also have some observations.
1) I noticed that without this little push I also lost some rebound so this skiing feels more fluid but also feels less dynamic, if I try to make it more dynamic, extensions returns back.
2) Now when I start a turn by transferring weight to old uphill ski all the work is done by my glutes (more) and quads (less) since old inside leg is still flexed when I transfer weight to it. And these muscles turned out to be weak as after 8 hours of such skiing they became really sore. I think it makes sense, being tall and rather skinny, without adequate workout on glutes it looks reasonable for me as I have never skied in a way that requires engagement of these muscles.
3) Tip lift to initiate a turn. This part is a bit tricky for me. I found that when I try to do it consciously, it disrupts my balance and fluidity of the drill. But when I try variation of SP when I release the ski earlier than across the fall line, more like 45 degree, it happens naturally due to ankle dorsiflexion that is held at the and of the turn (when I end turn across fall line, dorsiflexion is almost lost or not enough). Reflecting about nature of this unintended dorsiflexion, I think it appeared when I stopped lifting heel high so to keep inside ski a bit lifted with tail low I dorsiflex the ankle. So at the moment of transferring weight tip gets lifted due to tension of muscles that create dorsiflexion (I started realizing this tension once I noticed this). I tried doing this consciously but gave up since this is one more element that needs to be kept on mind and it displaces other important things.
3) CA/CB in pelvis. After some time I started engaging my pelvis into CA. What I quickly realized that it feels different than dryland exercises. It is feels like I move outer part of the pelvis outer and back so inner part goes inner and forward. As a result my inside foot goes forward which I don't like but continue doing it since this is the only what I can do with my pelvis for now. I also cannot create pelvis CB during slow SP on low pitch slope, only on steeper slope but than I cannot do CB and CA and tipping simultaneously.
Not sure if I do everything correctly, but just after one day working on SP transition, the idea to start new turn holding LTE is not more such weird. It feels more and more naturally.
Thank you, I should have been more attentive to details in the books and posted MA video earlier, just lost time.