I wish you well on this study and hope it will turn out info that will benefit us all. :)
I did want to say that I think both sides of the debate will say that it is based on scripture, and was defined by these two men who understood scripture differently. The definition of the two is merely used as a way to distinguish one set of beliefs from another. Much like we do when we encounter any person of another christian denomination than our own, except it may group certain christian denominations or beliefs together.
Of course you may be saying there is a third way to understand the different beliefs christians have that does not fit even within these two. There are all kinds of offshoots of christianity that would need their own category but I'm thinking you are not going that direction.
Most christians have no problems worshiping together...it's only when we try studying together or individually witnessing that we run into most of the differences.