Hey tt,
I have been thinking of your question since you posted it.
My first thought was no they are not related – but I am rethinking this.
I see my conscience as the part of me that knows right from wrong. It is the part of me that is the keeper of the tenets by which
I act towards other people. For example, one of the rules I live by is to do no harm, at all, unless absolutely necessary (eg., life-threatening situation). I have trouble stepping on an ant

. If I do harm then it is unintentional and reparation must be made.
I believe that my particular brand of voicelessness arises, at its most basic, from fear and from not trusting myself. For me it arises out of a feeling place, which to me is different from conscience. Where I am most voiceless is in
how I allow others to treat me.Although is it different? Perhaps conscience develops out of emotions to eventually end up dissociated from emotion (thinking about the Freudian model here – where we are born ids, and develop a superego [a conscience]).
In this way, I think voicelessness may contribute to the development of conscience, but eventually, conscience ends up as an entity separate from voicelessness - but nonetheless has been profoundly impacted by voicelessness.
IOW, using this one rule that I have – to do no harm - perhaps this rule (my conscience) developed because of the early environment that I lived in. I knew how badly I felt at being treated the way I was, and I refused to treat others this way, as I did not want to create that negativity in another person. I also had absolutely no control over others and learned at a very early age in a very warped world that the only control I had was over myself. So perhaps, my conscience is “wrongly-shaped” as it is one-sided. Perhaps a “rightly- shaped” conscience allows for rules for both how you treat others and for how others may treat you.
I don’t know the answer – but what a thought-provoking question!
Peace
PS. If any of this makes sense it is a miracle – curse of the INTJ I think, can see it, but have a hard time putting it into words! (Also - haven't even started to think on the other variables you pointed out - will, intellect,...)