My resolution for this all was to recreate the docker image using the previous apps feature. Rather than attempt the possible fate of resurrecting the nondeterministic behavior with custom networks I've decided to go whole enchilada with vlan tagging instead. This provides the desired network segregation similar to what I was getting with custom networks, but probably far more granular and likely enables possibilities that I'm not yet aware of.
Sn3akyP3t3's post in Unable To Start Docker Engine After Minor Update was marked as the answer