First, you have way too many points for a fit spline, if it was a control point spline, the more points the more the result will match you goal while maintaining a smooth curvature. I have a script that I created to recreate multiple connected splines into a single control point spline, why control points and fit? again to maintan a smooth result.
For your case, the creation of your spline as a fit point spline is symmetrical, so it shouldn't have more or less than a specific number of points (in you case 8 points), take a look at the attached picture below and notice that all angular tangent handles are symmetrical and equal, the same goes for the horizontal/vertical handles. This way, you get a symmetrical and smooth curvature comp.
The correct way to draw this is to create a circular pattern of a horizontal line so that you get a line every 45 deg intersecting with a projected line from your geometry, by this you'll have 8 points to snap to when creating your fit point spline.
Please find the .f3d file attached so that you can take a closer look.

Saeed Hamza
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