Best TimeMachine solution for macOS Sierra given current hardware?
If you buy the "Server" app from the App Store ($20 I think), it will let you once again use your iMac as a network based backup destination for Macs running Time Machine on the network. You can just turn on the Backup feature in Server.app and ignore all the rest. 

You can most likely do this without the server app using some command line tricks, but I don't know how off the top of my head. 

The only other solution is physically plugging in the drive to each Mac, one by one. But like you said, that's not ideal.