there are some instances in which I cannot lay the 2nd point down, even in the middle of a single face.

Is there a chance that there could be either a second edge or face laying practically on top of the one you are wanting to choose, preventing it from sitting there? I've had this happen when I tried to stack 2 things together, didn't snap them in place, combined them, then went thru the headache of trying to find which edge matches with which face. tedious to the extreme, lemme tell ya!