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It is not clear what your management wants for the representation of the curves in the imported drawing. To get a better feel for the shape I created short chords for several of the small mid-span splines (cyan curves) and then perpendicular bisectors (yellow). If you want to approximated the curve by arcs you could use the intersections of these bisectors as arc center points as you have discussed. However if you want to approximate the shape with a spline I would take the following approach. To simplify the task I will assume the shape is symmetric. The vertical cyan line is an approximate line of symmetry. Before creating the spline create a horizontal line at the top center vertex as shown below. The left end of the line will be the right most vertex of the spline and the left end of the line will be referenced to define the spline's tangency. This will ensure that the curve when mirrored will not have an inflection point at the top and will produce a smooth curve. Now create a spline using fit points that pass through points (going from left to right) on the spline segments. After clicking the right most point at the the centerline enter "t" for tangency and click the right end of the horizontal line. The result should look something like the following (magenta spline).

I think that no human drew this. There are odd bits of line all over the place!! Is this structural? It looks to me as if it could be an ellipsoidal lining of a tunnel. How important is the shape of it? I would go at it by drawing a polyline with the Nearest Object snap at suitable intervals and then curve fit.

Agree with you Steven P as I said in one of the other posts to RIA please provide all desired enhancements required rather than just changing the rules as you go and making new posts, this is very frustrating for us that are providing code.