No, unfortunately , it's not possible. The only way for WCF service to inform client about error it through soap fault message. Thus WCF service must follow soap specification.
Following specification all fault messages must have the same structure. See specification: SOAP 1.2, find section 5.4.6 SOAP Fault Codes. You can find and example (almost the same as you have provided) there and description of all the nodes.
In SOAP 1.2 was introduced Detail node (please refer to the specification: Section 5.4.5 SOAP Detail Element).
Providing your fault contract you can inject your custom error in xml form here (inside Detail element). But other xml structure is unchangeable.