The point I'm making is that a bridge across the AC still passes the current through the two AC connections when you draw current from the DC connections.
For example, if you draw 300mA from the DC output of the bridge, you are also drawing 300mA from the AC connections. So by using a constant current DC load you can maintain a constant current between the AC connections and it can be used in a series heater chain.
Equally, by maintaining a constant voltage across the DC connections, you can draw as much current as can be provided from the AC connections. With care you can satisfy the requirements of the heater circuit while still generating the DC supply needed for the isolating DC-DC converter.
Brian.