How can I remedy a multiple AirPort network where each base station tends to end up isolated from the rest?
The first thing I would suggest is to get an ethernet switch and place it between the ZTE router and the rest of the network.  Route all the Airport devices into the switch.  Then they should all see each other.  These cost $18-$25.  

I have two Airport Extreme Base Stations, at opposite ends of my house.  I set the one connected to a DSL modem to be the DHCP server, and create Airport wireless networks.  I select the channels manually, not automatic.  

The second base station is connected to the first by ethernet cable - not wirelessly.  It is set to bridge mode, but also to create wireless networks.  I give the networks the same, identical names, but manually select different channels than the first base station.  

This lets any WiFi device to connect to either server without any conflicts that I have noticed.  

You may wish to turn off the DHCP server on the ZTE router and use one of the Airport base stations to provide that service for your network.