Man, you got magic on your hand, why bother with trains (that or minimum build a functioning roman style roads), build jets, or something, heck build a space shuttle.
You're forgetting how insanely efficient trains are as transportation and Japan has mastered it.
I did an experiment with my brother where we found the road distance from Orlando, Florida, USA to New York, New York, USA and found the ETA by train, car, and plane. Did the same for a similar road distance route in Europe, and again in Japan.
USA and Europe had roughly equal Road to Train travel times with Planes being the much faster option. Japan's train was almost twice as fast as road travel and about a half hour to an hour slower than plane.
Trains are also much more efficient in terms of passengers/hour than Planes.
Given a 2-week travel time by carriage, which is ~30 miles/day, so ~420 miles between the two cities by carriage. A more direct route by train may cut off.... Let's say 20 miles for math's sake. Early steam trains could travel up to 50 mph under good conditions, so let's say it averages 40 mph, that's a 10-hour trip one way. If we go off modern Shinkansen speeds, that's between 160-200 mph, making it roughly a 2 hour trip between the cities, planes arent going to be needed for that short of a distance.