Well this saga isn't over yet.
My old Windows 2008 R2 KMS server is still up and running, has KMS installed, but is NOT published in DNS - I've confirmed this.
But when I went to a computer and ran
cscript slmgr.vbs /ato
to force a re-registration, it still registered with the old server.
Now I've disabled the port (1688) on the old server. Now to see how the client PCs handle that.