Best database replication technique for a very unstable (power wise) network
If MySQL isn't a hard requirement, consider FoundationDB Key-Value Store + SQL Layer.

FoundationDB is a distributed Key-Value database with ACID guarantees and strong fault-tolerance. You can setup a cluster spread across the different municipalities, and if a server in the cluster goes down, the rest of the cluster continues to operate and accept writes. Changes are automatically synced to the downed node once it comes back online.

Here's a video where you can see this in action: Dave is killing the power to different nodes in the cluster, and demonstrating the cluster remains up and accepts writes. This blog post walks through what happens to the database in the case of a network partition and adds more technical context.

SQL Layer is a process that maps SQL statements to the Key-Value Store. It which presents a full, ANSI-compliant SQL API to your application.

Full disclosure: I'm an engineer at FoundationDB