Whoa there little Besoeker Buckaroo! (Sorry, couldn't help myself
) Are you, as a fellow electrical engineer, honestly suggesting that the electrons are suddenly reversing themselves when they get to that mythical midpoint in the transformer? Do they go zipping along on their merry way down the wire, and then they suddenly see this big red stop sign in front of them at the center tap, and say, "oops, we can't go any farther this way, we gotta turn around and go back the other way"?
I hope you're not, because that is how your words are coming across in your posting.
The 180? phase shift exists
only because you have
hidden the negative sign caused by reversing the polarity of the power source's reference. If during your circuit analysis you fail to acknowledge (or discover) this hidden negative sign, then one half of the transformer's secondary coil will be a power source and the other will be a power sink (load). One half will have current opposing voltage, and the other half will have current conforming to voltage. These are electrical Laws that we are not free to break.
You are free to choose the personal preference of labeling your voltages A-N and B-N, but in doing so, you
cannot ignore the resulting negative sign from not choosing the A-N-B true convention of the
actual voltages. If you insist on using the 180? designation, then you
must include the negative sign with either your A-N or B-N voltage definition. Those two negatives must cancel out somewhere in your circuit analysis.