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This actually works. All you have to do is decelerate the train once (because it’s spinning with the world while you build it).
And solve the trivial engineering task of reducing all friction and air resistance to zero. Oh, and that of getting on and off the train.
You build your track dead straight - like, not conforming to the surface direct through the crust straight. Now the train accelerates downhill for the first half of the journey, and decelerates uphill for the second, neatly coming to a stop at the destination. Oddly enough, in the spherical cow universe where you build this, all the maths cancels such that you get a constant travel time regardless of the start and end locations. On earth it’s about 40 minutes
