The above is correct as far as it goes, what you are missing or ignoring is a language issue, not a physics issue.
You state 'L1 to N starting positive and N to L2 starting positive'; if one makes the perfectly reasonable choice of using N as the reference for your voltage measurements then the statement would read:
'L1 to N starting positive and L2 to N starting negative'
Using N as the reference reverses the sense of the measurement, but does not change the actual physics of the circuit. It is merely convention that the N terminal be used as the reference for the voltage measurement.
Selecting the N terminal as the voltage measurement _inverts_ the measurement of the sine wave. It does not create a new sine wave. It does not delay the sine wave by half a cycle. It does not change _single_ current flow at all; it simply inverts the measurement.
Now the final terminology issue: An inverted _single frequency_ sine wave is indistinguishable from a true 180 degree phase shifted sine wave. Not simply indistinguishable in the measurement, but also indistinguishable in the maths. Thus it is perfectly reasonable and common convention to call this apparent inversion a
180 degree phase difference. Do the vector math for the neutral current either way, as long as you select your current direction reference to match your voltage direction reference. Both approaches are internally self consistent.
The above does not change the fact that there is only a single current phase.
It simply means that calling one leg of the circuit 0 degrees and the other 180 degrees is common convention, and _works_ mathematically. Since the center tap is generally the grounded terminal of the transformer, and ground is commonly used as the voltage measurement, this is by far the most common convention.
Note, however the requirement for a pure single frequency sine wave. Add harmonics to the picture and the statement that inversion is indistinguishable and equivalent to a 180 degree phase shift no longer holds. If you continue to assume that an inversion is the same as a 180 degree phase shift you may get incorrect results in your calculation. But it is true for single frequency situations, and that is often good enough for AC power distribution.
-Jon