How can I remedy a multiple AirPort network where each base station tends to end up isolated from the rest?
Solution 1:
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.
Solution 2:
Apple's free roaming network with their AirPort and Time Capsule routers works great... as long as you're using one of their devices as the master DHCP server and link to the DSL modem.
Once you switch from "Extend a network" into "Bridge" mode, you lose all ability to free roam.
At both my parent's home and my office I have the DLS modem (the ZTE ZXDSL in your case), a switch (can be built into the modem) and various AirPorts and/or Time Capsules.
Turn off all the Apple routers except one and start with that one. Configure it to be the main link and the DHCP server. Make sure it talks to the internet and does everything you want.
Next, configure the next Apple wireless router. Sometimes you need to reset them back to baseline configuration and then begin from there. As it comes up, use the wizard to select "Extend a network" and follow the prompts to input the info for your network. Make sure everything works to connect to the internet with both Apple routers.
Repeat the procedure with the third.
Having the AirPorts hard-wired together provides the best infrastructure between the access points.
Enjoy your free roaming.