TryingTo"Unroll"ClosedCurve

I am hoping someone has words of advice as to how to unroll a closed curve and end up with a straight line with tabs that correspond to the closed curve.

I am most of the way there, but stuck on finding a way to adjust the tab locations.

Their position along the line needs to correspond to the closed version, but it would be great if I could shift the results so that a tabbed area isn't at the beginning or end of the line.

I manually adjusted the white colored line to indicate what I would like to do in GH.

I know that the Tab geometry is different in shape that the arcs along the closed curve, but the t values for their location should be the same.

Thanks for any insights!