Convert outline stroke to single line

I need to take an image where the strokes outline the lines when filled and convert them into a single line.  The end result is that I would like the lines to be a certain thickness (1/32") so that I can use this for stained glass.

Here is a portion of the source:

I want to have the lines shown in the below image to be of a certain size.   Shown below is an gross  example (rasterized) of what I'd like have, but with slimer (1/32") lines.   I want to keep the vector representation of course so that I can resize to the desired size while keeping the lines that same width.

To be precise, I'd like to take the original image and convert the two strokes that outline the shape into a single stroke at the midpoint between the outline strokes.

How would I go about doing this.  It doesn't have to be precisely the midpoint.