Could you please confirm my method or correct me on computing the phases of my signals?
As Marcus Müller says, phase is relative.  Consider the Discrete Fourier Transform equation:

$$X[k] = \sum_{n=0}^{N-1}x[n]e^{-j2 \pi nk/N}$$

The DFT at element $k$ is the inner product of the signal with a complex exponential with frequency $2{\pi}k/N$ cycles/sample and an initial phase of 0.  Thus the phase of element $k$ is the phase difference of a particular frequency component of the signal relative to a particular complex exponential.

The equation you referenced is the phase shift of a single tone that travels a distance $L$.