WCF IErrorHandler to return FaultException to SOAP and WebHttpException to POX and Json endpoints

I have a set of SOAP webservices that are wrapping exceptions using IErrorHandler, specifically:

public sealed class ErrorHandler : IErrorHandler
{
    public bool HandleError(Exception error)
    {
        return true;
    }

    public void ProvideFault(Exception error, MessageVersion version, ref Message fault)
    {
        // don't wrap existing fault exceptions
        if ((error is FaultException)) return;

        // our basic service fault
        var businessFault = new BusinessFault { FaultMessage = error.Message, FaultReference = "Internal" };

        // Resource based faultReason
        var faultReason = new FaultReason(Properties.Resources.BusinessFaultReason);
        var faultcode = FaultCodeFactory.CreateVersionAwareSenderFaultCode(InternalFaultCodes.BusinessFailure.ToString(), Service.Namespace);

        var faultException = new FaultException<BusinessFault>(
            businessFault,
            faultReason,
            faultcode);

        // Create message fault
        var messageFault = faultException.CreateMessageFault();

        // Create message using Message Factory method
        fault = Message.CreateMessage(version, messageFault, faultException.Action);
    }
}

I have now added extra endpoints for Json and Pox which work fine, unless an exception occurs. In the case of the Json endpoint the FaultException is returned as XML.

I am aware from other SO posts that in the case of REST I would be better throwing a WebHttpException:

throw new WebFaultException<BusinessFault>(detail, HttpStatusCode.BadRequest);

Or overriding the response message properties in ProvideFault, thus:

var wbf = new WebBodyFormatMessageProperty(WebContentFormat.Json);
fault.Properties.Add(WebBodyFormatMessageProperty.Name, wbf);

var rmp = new HttpResponseMessageProperty
{
    StatusCode = System.Net.HttpStatusCode.BadRequest,
    StatusDescription = "See fa