Transfer function of phase change controlled with capacitance
The phase change due to capacitance is not set in stone for all applied frequencies. For instance at resonance (current is maximum) the phase rapidly changes 180 degrees over a very small band of frequencies.

At higher or lower frequencies (nowhere near resonance) the phase change hardly moves at all unless the quality factor (Q) of the circuit is very small. Altering C at these extremes has very little effect on phase change.