Stanley, your explanation does not address the engineer's concern. Read again, below.
Actually it does.
If the prescribed curvature was indeed as represented, the central stations at Rugby or Warwick ought to be close upon three miles higher than a chord drawn from the two extremities. If such was the case there is not a driver or stoker within the Kingdom that would be found to take charge of the train.
The first sentence is true. A chord (line) drawn between two points on a circle will be inside the circle.
However, the second sentence does not follow.
The force of gravity increases with decreasing distance from the center of gravity. Gravity is lower at higher altitudes and higher at lower altitudes.
But every point on a circle is the same distance from the center of the circle. If the earth were exactly a sphere, then every point on earth would be the same distance from the center of the earth and experience the same magnitude of gravity though the direction would be toward the center of the earth.
Thus the engineer's concern is mistaken. All points at the same distance from the center of the earth are at the same gravitational "level". There is no grade up or down.
However, if you did have a straight line tunnel (a chord) running between two distant cities, points in that tunnel would be closer to the center. Travelling that tunnel would involve a grade down to the midpoint, and then a grade up, as far as gravity is concerned.