ok, I think I understand. By definition, if you are continuing to look downhill as you progress through toeside, you are counter-rotating. I'm thinking that you don't need advice on snowboarding, but rather you need advice on fear management

I think you already know that your technique is not correct, and you know the correct technique, you just can't bring yourself to do it.
So this advice may turn more philosophical than technical
Getting over fear is counter-intuitive. Our bodies and minds react to things in order to protect us from harm. We tend to fear things that will hurt us. Now, there are rational fears and there are irrational fears. Philosophers say that what separates humans from animals is that we can "think about thinking." We can control our fears, sometimes just mentally. It's not easy, and sometimes it's not wise. For example, we are afraid of jumping off of a bridge. Sure, you could convince yourself that you were not afraid, but that would be dumb because then you'd die!
Here, with snowboarding, you have seen this done. You know that other people go toeside and don't catch their edge. So this is a scenario where your fear is (to some degree) irrational. You can conquer this fear. There are tons of mental tricks you can use, I have my own personal ones that I use to conquer fear - so I can really only tell you what works for me.
Get some protective gear, at least a spine protector and some knee pads. Having pads on, at least for me, really helps my confidence level because i know if I fall, it wont hurt as much. Remember your safety net - you are so close to the snow that if you fall, it wont matter. Also, the lower you go, the less chance your heel has to catch. Another way to help fear is to approach things slowly. Set up drills for yourself where you slowly start to look up hill. Just do one turn, stop, then do another turn. Each time try to rotate just a little more, and try to look uphill just a little more. Go back to basics - don't try to lay out or get as low as possible, just do some nice, easy toeside turns on a green where you feel comfortable, making sure that you are rotating correctly.
Everyone has their fears and noone is ever an expert instantly. Even the best riders were beginners once and had their own demons

to slay.
It's not whether you can do it, it's whether you give up before you can.