Determination of System poles through open/short circuit time constant technique
From your own source, and partly from my memory of Zero-Value Time Constant Analysis calculations, you seem to be confused about Dominant Poles, Non-Dominant Poles, and Bandwidth.

1) What you state as the Dominant pole calculation is actually the bandwidth calculation. (omega -3dB) = 1/(summation of all times constants)

2) Dominant poles are the pole who's time constant is at least one decade below the other poles. (Literally took this from the bottom of the linked page)

3) Non-Dominant poles are ALL other poles that are not dominant (per definition).

Taking these correction into account, simply calculate the three poles (three capacitors, three poles) using your short-circuit analysis (ZVTC, as I was introduced to calling it). If one of the pole fits the definition of a dominant pole, then the other two poles are the non-dominate poles. If no pole is dominant then there are three non-dominant poles.