Rather than use component-scanning to redefine the bean, remove that annotation and do it via XML instead.
So your class definition would change to:
public class MyCustomerStateRequestProcessor extends
CustomerStateRequestProcessor {
...
}
And then in any of your applicationContext.xml files (except for the servlet one) add this:
<bean id="blCustomerStateRequestProcessor" class="com.yourcompany.site.web.MyCustomerStateRequestProcessor" />
Note that this pattern is the same for overriding any Broadleaf-defined beans.