Just for fun, and using the Perl TMTOWTDI philosophy (โThere's more than one way to do thisโ), I extracted all the white points of your outlines into a file called points.dat and submitted it to gnuplot to fit the curve that gave me the formula for best line of compliance:
y=3.10869110524588e-07*x*x*x -0.000972406154863963*x*x + 0.861790477479291*x + 307.220397010312
And then I painted this in red on your source paths using awk and ImageMagick .
#!/bin/bash convert contours.jpg -colorspace gray -threshold 50% txt: | awk -F: '/white/{print $1}' | tr ',' ' ' > points.dat { echo 'f(x) = a*x**3 + b*x**2 + c*x + d'; \ echo 'fit f(x) "points.dat" via a, b, c, d'; \ echo 'print a,"*u^3 + ",b,"*u^2 + ",c,"*u + ",d'; \ } | gnuplot 2>&1 | tail -1 awk 'BEGIN{ for(x=0;x<1504;x++){ y=3.10869110524588e-07*x*x*x -0.000972406154863963*x*x + 0.861790477479291*x + 307.220397010312 y=int(y) print "point ",x,y } }' /dev/null > p.mvg convert contours.jpg -draw @p.mvg z.png

The beginning of points.dat as follows:
769 453 770 453 771 453 772 453 773 453 769 454 765 455 766 455 767 455 768 455 ... ...
The beginning of p.mvg as follows:
fill red point 0 307 point 1 308 point 2 308 point 3 309 point 4 310 point 5 311 point 6 312 point 7 313 point 8 314 ... ...
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