The little glitch will be much smaller when a decent number of points is chosen. They should be much closer together where the curvature is higher to better follow the surface.
I thought there was a way to have the spline ends tangent to a construction line. If your shape is symmetrical, that construction line is perpendicular to the plane of symmetry. Maybe the deal was to sketch line segments on either side of the plane of symmetry, establish tangency, and then convert them to construction entities.