The derivation is clean. The conclusion is a little stronger than the maths supports though, and the gap is the interesting part.
Two different things are bundled into your 56 ms. The speed of light is a law. The refractive index of 1.5 is an engineering choice, and it is actively being removed: hollow-core fiber guides light through air rather than glass, so its index sits near 1.0, worth roughly a third off transit time. It is already deployed on latency-sensitive financial routes. So that half of the number is not physics, it is the current generation of glass.
The other half cuts the opposite way. 56 ms assumes a great-circle path and no cable follows one. Transatlantic routes bend around seabed terrain and landing sites, so the real floor sits meaningfully above your figure before any switching or queuing is counted.
The version I would defend: about 37 ms is the floor set by c, 56 ms is the floor for glass on a path nobody can build, and a real connection lands above both. Only the first is a law, and separating them makes the physics claim stronger rather than weaker.