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Two problems with this (except the practical matters you've
highlighted):
1. The approximation that a pendulum's period is independent of its
peak deflection only applies for small deflections, i.e. short journeys
in terms of your train.
2. If moving under gravity alone, it would take a very long time for
short journeys and longer for long ones (see point one), so you'd be
wise to power (and brake) your train like a regular one.
However, I'm pretty sure it would be quicker, for a given energy input,
than a train travelling on the surface, so it's not totally without
merit.