Automatic path/line in the center of the letter

And just to be a bit fair and realistic: The New Year Strokes approach was by no means provided to create the centerlines of (outlined) type objects / calligraphic type objects.

It was rather meant to recreate (single) stroked paths out of outlined stroked paths, as can be seen in floorplans, technical drawings or network maps, for example.

Omar,

In addition to what Monika said, one complication often encountered as in your case is that  parts of your centre lines where they cross each other are without guides in the letter shapes because the corresponding parts of the original (grey filled) paths have been lost by uniting them.

If you could go back to those original paths, it would be much easier (albeit non automatic), using a bit of preparation and then a 1 step Blend (maybe with a bit of adjustment), especially because your centre lines do not extend into the rounded end parts.

The long answer is no.