I think for me the fastest way would just be to loop cut each line, eyeball it as close as possible, and then merge the vertexes. 

I just looked at using a boolean op, but it doesn't see to work well for just edges. 

If someone else has a better method, I'd be interested in hearing it as well. 

Good luck.

Reddog9
Tutorials, Samples and Models
www.blender3dclub.com