Best method alter curve to snap it to 3 black points and keep CP locations Y axis?

My red curve has a control point distribution along it for a half cosine aerofoil and I dont want to lose that, but it needs to pass through 3 black points.
see attached.

I can tweak those cp’s up/down, moving them up/down in the y axis is ok to keep the cp distribution, to visually pass the curve through the black points, but I seek a better snap to method as visual is not playing the game and further zoom in will see a ‘miss’. Start and end points of curve must not move.

Did I do well ?..I have opted for add edit points to curve at locations of black points then drag snap to black, then curvature graph tweak with control points active instead of edit pts and gumball set to 1 on strength, in fact I normally use nudge 0.01 or finer so maybe 0.1 on strength if possible. Is this best curve approach ?

AlterCurve Not spacing of control points.3dm (26.5 KB)