It doesn't seem like you are doing anything wrong. Rather it seems you are getting results, you now are becoming more aware of the difference between being aware and not aware.
Might there be some confusion on which aspect is the real or source of you? You say you are aware of being conscious, of yourself (not of unconsciousness) and it feels very heavy and intense. If you mean heavy and intense, such as negative and unwanted and feeling crappy, then it must be you are noticing how it feels to be as the talking/emoting self, unconsciousness, or ego. If rather you mean by heavy and intense, that it feels like you are falling into a deep sleep, or you have the feeling of losing yourself in a cloud of strong energy, having nothing to hang onto which is familiar, then this can be a sign of your source self, consciousness emerging. It is normal that fear is felt the first few times this phenomena happens, but also it feels blissful, not heavy and not intense. This is because it happens when you are totally quiet in mind and emotions, thus at the exact moment it happens there are no qualities, such as heavy and intense. It is usually fear of losing the 'old self' or 'old way', that takes one out of the quiet blissful feeling.
To transform, to raise awareness and go beyond your personality it needs a big ego, because this is the source of energy, that is used to fuel the transition. The bigger the ego, the easier it is to see when it arises and takes over and becomes the predominant energy, meaning one is lost in the old acting mode and has lost presence. So see a big ego, as beneficial, as something that can help you detect for sure when you are and when you are not.
I come from background of analyzing everything too, it's a good challenge to go beyond, perfect for you, exactly what you need. So it seems to me your challenge is to become better at discerning when you are truly quiet and when you are not, and what qualities or symptoms does it present in your body when in the two different states. Learning to tell the difference between them, by observing what you can see, can be your beacon in the dark.