So let them sink! Skiing the deep is about subtly, smoothness, and balance. You don't have to float on top to enjoy it. Quite the opposite actually.
BTW: why would you dead center mount Lizzies anyway? Your weight should be over your toes, not your midfoot. Even mounting symmetrical skis at dead center makes no sense. Once you lean to engage your boots, your well past the center of the ski, your tails wash out, and you are forced back to maintain balance, leading to shin bang, and poor skiing.