Here is the code, based on Femi's answer.
It can be a little tricky to figure out. Works beautifully!
Service jaxwsService = Service.create(wsdlURL, serviceName);
Dispatch<SOAPMessage> disp = jaxwsService.createDispatch(portName, SOAPMessage.class, Service.Mode.MESSAGE);
//Add HTTP request Headers
Map<String, List<String>> requestHeaders = new HashMap<>();
requestHeaders.put("Auth-User", Arrays.asList("BILL_GATES"));
disp.getRequestContext().put(MessageContext.HTTP_REQUEST_HEADERS, requestHeaders);
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