You’re right. PJ and myself and the physics writers you mention are on the same page. The problem is that other popular discussion of side refers to tips of english and each are in relationship to the ghost ball line. My first point is that the distance the cue line is from center is the actual lever turning the ball. As long as we discuss old misconceptions and perspectives we learn nothing new.
Now to the new. I mentioned moving off the target line and then pointing the cue line back towards center. Imagine moving the cue line back towards center but not all the way. So imagine moving the width of two dimes away from center then pointing the cue line back half that distance, the width of one dime. Notice where the cue is pointing in relation to the original cue line, it now crosses onto the opposite side of the original cue line. NONE of the present parallel english, FHE or BHE methods of applying side converge back towards the shot line, they ALL diverge. So two new labels enter the conversation, divergent and convergent english. Here is the blasphemy, I’m using the ghost ball line as the reference line, because it is the aim line understood by a majority of players. Even Dr. Dave with his SAWS program uses the deflection adjusted ghost ball line as a reference then following that with a distance/pace adjusted combination of BHE and from the new back hand position a sweep with the front hand to a pre-calculated ratio final position. He recognizes the ingrained, although incorrect perception, of using the ghost ball line. He uses a known reference as a starting point. In that spirit, the terms divergent and convergent are cue line relationship terms relative to an adjusted ghost ball aim line.
This is the second insight, the cue line can be pointed back to and cross the original aim reference line, generating side on a convergent rather than divergent path.
If I understand you correctly (which I'm sure I'm not, because there are some confusing terms), and we were on a table, it reads like your method is awfully similar to mine. And I try not to describe mine in these or any groups because it's too confusion to put on paper.
The highlighted sentence, ... I"m sure you're incorrect, but again, I'm only guessing at your definition of "converge to the shotline."