I finally got it working. Essentially I did inject everything by Field Injection (In my usecase I had cyclomatic injections, which are not supported in Errai). So everything could get wired up at startup time.
The problem with ExtGWT MVC Framework was easy: In my View Class I just called the super constructor with null and Injected the Controller. I created a @PostCreation method wich set the super Controller instance to the injected controller. (This was possible, since the Controller had protected scope.).
So essentially the problem is the ExtGWT MVC Frameworks architecture. What I did is just a workaround, but no solution for a complex application, since the ability to lazy load views is lost.
Thanks @csadilek for helping me with my issue on IRC.