Integração de Spring com EJB

Estou tentando montar um projeto do zero utilizando Spring e EJB com base nos cursos que fiz no Alura.

Fiz toda a minha configuração do meu Datasource via standalone e utilizei as configurações do hibernate via persistence.xml. Criei minhas classe Entity, e as defini no persistence.xml. Até aqui tudo OK, quando inicio meu AS as classes são lidas e as tabelas são criadas.

Minha Entity:

@Entity
public class User {

    @Id
    @Column(nullable = false)
    private String userName;
    private String password;
    @Enumerated(EnumType.STRING)
    private UserRole userRole;
    private Date lastLoginDate;
    (...)

Quando cheguei a parte de criar meu DAO comecou a saga. Primeiro tive problema de incompatibilidade entre o dom4j, consegui resolver desabilitando a opção do Envers na configuração do hibernate. Até então OK!

Criei a classe do DAO como EJB @Stateless, e utilizo a annotation @Inject dentro da minha classe Controller para fazer a injeção do EJB. E quando dou o deploy da applicação, aparece o AS carregando o DAO na memória

Meu DAO:

import javax.ejb.Stateless;
import javax.persistence.EntityManager;
import javax.persistence.PersistenceContext;
import javax.persistence.criteria.CriteriaBuilder;
import javax.persistence.criteria.CriteriaQuery;
import javax.persistence.criteria.Root;

import com.fogsoft.myapp.exceptions.DuplicateEntityException;
import com.fogsoft.myapp.model.User;

@Stateless
public class UserDao extends AbstractDao{

    @PersistenceContext
    private EntityManager em;

    public User getUserByUsername(String username) throws IllegalArgumentException{
        if (username.isEmpty()) throw new IllegalArgumentException("Username is required");
        (...)

Console do AS:

(...)
23:04:19,378 INFO  [org.jboss.as.ejb3.deployment] (MSC service thread 1-7) WFLYEJB0473: JNDI bindings for session bean named 'UserDao' in deployment unit 'deployment "MyApp.war"' are as follows:

    java:global/MyApp/UserDao!com.fogsoft.MyApp.dao.UserDao
    java:app/MyApp/UserDao!com.fogsoft.MyApp.dao.UserDao
    java:module/UserDao!com.fogsoft.MyApp.dao.UserDao
    java:global/MyApp/UserDao
    java:app/MyApp/UserDao
    java:module/UserDao

23:04:20,394 INFO  [org.jboss.as.connector.deployers.jdbc] (MSC service thread 1-7) WFLYJCA0005: Deploying non-JDBC-compliant driver class com.mysql.jdbc.Driver (version 5.1)
(...)

Meu Controller:

import javax.inject.Inject;

import org.springframework.stereotype.Controller;
import org.springframework.web.bind.annotation.RequestMapping;

import com.fogsoft.myapp.dao.UserDao;
import com.fogsoft.myapp.model.User;

@Controller
public class UserController {

    @Inject
    private UserDao dao;

    @RequestMapping("/user/add")
    public String addUserForm() {
        return ("User/add");
    }
    (...)

Consigo compilar e dar deploy da minha aplicação. Porem ao acessar a url do meu Spring onde vou fazer o cadastro do registro recebo a seguinte Exception:

Context Path:
/MyApp

Servlet Path:
/user/add

Path Info:
null

Query String:
null

Stack Trace:

org.springframework.beans.factory.UnsatisfiedDependencyException: Error creating bean with name 'userController': Unsatisfied dependency expressed through field 'dao'; nested exception is org.springframework.beans.factory.NoSuchBeanDefinitionException: No qualifying bean of type 'com.fogsoft.MyApp.dao.UserDao' available: expected at least 1 bean which qualifies as autowire candidate. Dependency annotations: {@javax.inject.Inject()}
    at deployment.MyApp.war//org.springframework.beans.factory.annotation.AutowiredAnnotationBeanPostProcessor$AutowiredFieldElement.inject(AutowiredAnnotationBeanPostProcessor.java:586)
    at deployment.MyApp.war//org.springframework.beans.factory.annotation.InjectionMetadata.inject(InjectionMetadata.java:91)
    at deployment.MyApp.war//org.springframework.beans.factory.annotation.AutowiredAnnotationBeanPostProcessor.postProcessPropertyValues(AutowiredAnnotationBeanPostProcessor.java:372)
    at deployment.MyApp.war//org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.populateBean(AbstractAutowireCapableBeanFactory.java:1344)
    at deployment.MyApp.war//org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.doCreateBean(AbstractAutowireCapableBeanFactory.java:582)
    at deployment.MyApp.war//org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.createBean(AbstractAutowireCapableBeanFactory.java:502)

O que estou fazendo de errado? Posso fazer essa integração? O que li sobre o Envers seria algo para auditoria, pode ser a falta desse recurso a causadora desse problema?

Estou utilizando Java8.0_152, Wildfly 10.1, Spring 5.0.2, Hibernate 5.2.12 e MySqlConnector 5.1.31