I'm sure everything you write is true
BUT From the wiki page on
Electric CurrentA flow of positive charges gives the same electric current as a flow of negative charges in the opposite direction. Since current can be the flow of either positive or negative charges, or both, a convention for the direction of current which is independent of the type of charge carriers is needed. Therefore the direction of conventional current is defined to be the direction of the flow of positive charges.
I'm using the conventional current notation.