I've completed characterization of the "after dark" prototype boards, and the FR4 material has significantly lower relative permittivity than the standard purple boards.

Performing a regression between the length and resonance period yields a fairly clean result:

This indicates that the phase velocity is 0.1685 m / ns which results in a relative permittivity of 3.164:

In summary:

• purple boards: 4.202 relative permittivity
• after dark: 3.164 relative permittivity