Push and pull.

Be crouched between turns, extend during the first half of the carve, compress during the second half. The steeper the slope and the further you lean, the more helpful it gets.

The reasons that it's so helpful are subtle but real. When initiate a carve on a steep hill, you're engaging the downhill edge, and your center-of-mass starts falling down, so your edge pressure is lower. Extending your legs helps with that.

When you're in the middle of a carved turn on a steep hill, you accelerate. Compressing your legs in the second half of the turn helps to absorb some of that speed, so that you can return to a reasonable speed before you start your next carve.

Also if you haven't tried some different sidecut radius boards, you probably don't know what you're missing. Soft booters, especially. It's easy to find alpine boards from 10 to 20 meters but the soft boot world rarely goes above 10m, and 10 is the MINIMUM for fun carving IMO. My shortest is 11.5. I mostly ride 13, and 15-16m is where it starts feeling a little bit too large for my taste. But I still ride those 15+ boards a couple times a year because it's a fun change of pace.

If you've never carved with a sidecut radius over 10 meters, you owe it to yourself to try something in the 12+ range. It'll be harder at low speeds, but it'll be easier to ride at high speeds.

You might find that your old board feels too twitchy when you go back to it. You might find that after you get confident with the speeds required by a larger sidecut, your old board doesn't even function properly until you slow down. You might find that your old board was holding you back. But eventually you'll find that you can do anything on any board, it's just easier on some boards than on others.