Spring + JPA + multiple persistence units: Injecting EntityManager

I need to use one database for queries (non-modifying) and one for commands (modifying). I am using Spring Data JPA, so I have two configuration classes:

@Configuration
@EnableJpaRepositories(value = "com.company.read",
        entityManagerFactoryRef = "readingEntityManagerFactory",
        transactionManagerRef = "readingTransactionManager")
@EnableTransactionManagement
public class SpringDataJpaReadingConfiguration {

    @Bean(name = "readingEntityManagerFactory")
    public EntityManagerFactory readingEntityManagerFactory() {
        return Persistence.createEntityManagerFactory("persistence.reading");
    }

    @Bean(name = "readingExceptionTranslator")
    public HibernateExceptionTranslator readingHibernateExceptionTranslator() {
        return new HibernateExceptionTranslator();
    }

    @Bean(name = "readingTransactionManager")
    public JpaTransactionManager readingTransactionManager() {
        return new JpaTransactionManager();
    }

}

@Configuration
@EnableJpaRepositories(value = "com.company.write",
        entityManagerFactoryRef = "writingEntityManagerFactory",
        transactionManagerRef = "writingTransactionManager")
@EnableTransactionManagement
public class SpringDataJpaWritingConfiguration {

    @Bean(name = "writingEntityManagerFactory")
    public EntityManagerFactory writingEntityManagerFactory() {
        return Persistence.createEntityManagerFactory("persistence.writing");
    }

    @Bean(name = "writingExceptionTranslator")
    public HibernateExceptionTranslator writingHibernateExceptionTranslator() {
        return new HibernateExceptionTranslator();
    }

    @Bean(name = "writingTransactionManager")
    public JpaTransactionManager writingTransactionManager() {
        return new JpaTransactionManager();
    }

}

In my repository I sometimes need to decide with EntityManager to use like so:

@Repository
public class UserReadingRepository {

    @PersistenceContext(unitName = "persistence.reading")
    private EntityManager em;

    // some useful queries here
}

I am using persistence unit's name as defined in my persistence.xml:

<persistence xmlns="http://ift.tt/UICAJV"
             xmlns:xsi="http://ift.tt/ra1lAU"
             xsi:schemaLocation="http://ift.tt/UICAJV http://ift.tt/O9YdEP"
             version="2.0">

    <persistence-unit name="persistence.reading" transaction-type="RESOURCE_LOCAL">
        <provider>org.hibernate.jpa.HibernatePersistenceProvider</provider>
        <non-jta-data-source>ReadingDS</non-jta-data-source>
        <properties>
            <property name="hibernate.dialect" value="org.hibernate.dialect.MySQLDialect" />
            <property name="hibernate.show_sql" value="true" />
        </properties>
    </persistence-unit>

    <persistence-unit name="persistence.writing" transaction-type="RESOURCE_LOCAL">
        <provider>org.hibernate.jpa.HibernatePersistenceProvider</provider>
        <non-jta-data-source>WritingDS</non-jta-data-source>
        <properties>
            <property name="hibernate.dialect" value="org.hibernate.dialect.MySQLDialect" />
            <property name="hibernate.show_sql" value="true" />
        </properties>
    </persistence-unit>

</persistence>

Spring throws org.springframework.beans.factory.NoSuchBeanDefinitionException: No bean named 'persistence.reading' is defined. Oddly, it looks like Spring tries to instantiate a bean with persistence unit name? Did I misconfigure something?