As you have discovered, working with splines can be very fussy and maddening. For your particular example, placement of the splines points is critical. Try initially placing your points as close as you can to the points in the original spline. If you start out with them spaced far away from the final point, the spline distorts as you try to shove them together.
More critically, I suspect that the original spline has perpendicular relationships at the two ends. The top end is probably perpendicular to the arc across the top and the lower end is probably perpendicular to the vertical construction line on the left.
Personally, I would see if you could get by with only three points in the middle, as I usually have better luck with the minimum possible number of spline points.