If you need to do this repeatedly, have Visio, and can do some VBA, you
might consider the followng:

Copy the chart into the clipboard, open Visio, new document, paste.

Ungroup the object.

Write a VBA program to iterate through the objects (there are basically
lines, text, and filled areas) and bring anything in the colour of your
line to the front. Or bring lines of colour x to the front and leave
text of colour x alone. Whatever you have to do to differentiate
between the two.

Save as metafile, visio drawing, whatever works. Most of my Excel
graphs wind up as lightweight metafiles linked to Word documents.

I have had a fair bit of success doing this kind of postprocessing in
Visio to achieve publication quality results. I have moved labels
around, done colour sorting (the line on top is most important but
needs to be drawn last), and so on. Most of this automates very
nicely.

At least, with Visio, you can gain some understanding of how Excel
draws. Then do something about it.