SOLUTION NOTE: Make sure to look at the final solution (after the one marked as answer)
Q: Does anyone know how to access the "target path" information from existing replicas? ....in a python script.
With the answer in my related thread where I use arcpy.da.ListReplicas("mySDEGDB" to get a list of all my replicas, and can extract attributes like the common name (vs how SQL lists it). However, it doesn't look like the "target path" is one of the attributes that I see as exposed. ListReplicas—Help | ArcGIS for Desktop
This will eventually be part a few tools in an addin.
Desktop 10.3.1 (soon 10.5.x)
ArcSDE 10.3.x - SQL 2008 (soon to be 2012, 2014 or 2016)
I have also submitted a tech support call, but have not heard anything back yet. My guess is it will take something more than arcpy.