You have to actually engage your legs and feet when you butter, you can’t just lean over. Best way I can describe it is that its almost a similar way to picking up an object off the floor with your toes (kinda but not really), you gotta push down into the ground with your toes and simultaneously lift your heels. This will massively reduce heel lift and give you more power. That way when you lean, your skis will actually come up, not just your body leaning over. I do a subtle pop to help get into it but that isn’t completely necessary, although I find it helps a lot.
One of, if not the biggest mistake you are making is that you don’t start pressing until almost 180 degress. I take pride in doin legit butters so I actually press and lean when im completely forwards still, but you need to be doing the press at a minimum of 90 degress. This is where doing a slight pop can help because you can almost think of it as jumping into it at 90 degrees at first. Using your leg muscles and feet will help not handdrag but it will take practice. Doing legit nosebutters are not easy. Last piece of advice is learning how to nose press going straight down hill. Its super scary at first but if you can do it legit for a couple seconds it will help massively. It forces you to do it with engaged legs and teaches you the balance point. Rather than guessing every time
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Here is example of you not being pressed at min 90 degrees
Good luck!!