I have attached a python file that was exported from Model Builder that created the output shown for a set of Southern California Counties. It creates a non-overlapping external buffer that is 1 mile wide. It requires an Advanced license to use all of the tools I applied in the model.
One picture shows the rather complex coastline where Los Angeles and Orange Counties meet which illustrates how well the model worked.
While Yuma and Imperial Counties do not really have a coastline, I used them to illustrate one problem I resolved. The extension of the internal boundary between these two Counties ran parallel to the buffer boundary. If I had done a normal line extension Yuma County would contain most of the zone that ran in front of Imperial County. To resolve that I contained the interior boundary extension to fit within a buffer only surrounding the interior boundary lines that was at a 3 to 1 ratio with the full outer polygon boundaries. Not the perfect division, but it was acceptable.
The second issue shown that I did not resolve involved an Island of Ventura County where the Centroid of the Island Buffer did not fall within the actual Island polygon. This made it not take on the island's data when I ran the Spatial Join with that join criteria. A special process would have to be added to handle this special situation, but I think with a select by Attribute and a secondary process it could be resolved.
A final problem not shown and not resolved is the issue of two parallel original polygon boundaries that do not touch and that are close enough together that their buffers would merge. This is similar to the problem with internal boundaries being parallel to the buffer boundary, but in reality this does not involve the internal overlapping boundaries. It involves creation of a Centerline between the two parallel boundaries to create a division in the buffers. I don't know if the tools in ArcGIS are good enough to handle that situation and it did not come up with this particular data.
Anyway, I hope this gets you closer to what you want.