In my opinion, this is more of a motor pattern issue. You said the issue is "more prominent" when lifting heavier weights. If this is something that's happening from the moment you begin to warm up, I would strongly recommend returning to basics for a period of time. You're compounding that motor pattern and making it a habit -- you need to break away from that. Simple footwork drills, like going to your toes and then repositioning into a receiving stance ready to squat, will help you learn the right movement.
Then, I recommend doing some tall snatches with just the bar or even a PVC pipe/dowel. The reason for that recommendation is in order to effectively pull under in a movement where the bar isn't accelerating upward, you're going to have to aggressively move the feet FIRST. When first trying this, most people will have a tendency to laterally shift their feet in a simple manner. You can avoid this (and the ensuing frustration) by lifting -- not hinging as to promote a donkey kick -- at the knees, then firmly planting your feet into your receiving position. This is an aggressive movement (and one of the progression drills) that will teach you speed under the bar, on top of getting comfortable and consistent in your footwork.
As you continue to get more comfortable, you can start to add the weight back on and go back into hang/block snatches, and eventually taking the bar from the floor. The "return to basics" portion doesn't necessarily mean that you're stripping all the weight off the bar, but if you're body is not positively responding to the drill, then the weight may be a little too heavy. Remember, perfect practice makes perfect, so ensuring that you have a manageable training weight is important.
Hope this helps,
Javier A. Sanjuan
Olympus Barbell Club
Dear God, please help me lift heavy and be awesome. Thanks. Amen.