Heavy overhead squats and snatch balances - develop the strength and stability in that bottom position, and you'll find you'll be much better able to pull under heavier weights. Arden's suggestions are also good.
Keep in mind as well that even the heaviest snatches will not actually be received in a full squat - they'll be received higher and ridden down into the bottom. That said, there needs to be a smooth transition between those two points, and that's something that comes with experience and time.
Keep working that bottom position with heavy weights, keep working the light technique and speed drills, and keep forcing yourself to pull under the bar. Just do it.