About a year ago I tried to create a build with gradle and appengine and after a day of trying various options I gave up. At the time I was working for a Company that also did a lot of Groovy and Grails work and there were a lot of experts around. There is still a lot of development going on so maybe nowadays it's easier. In the end GWT compiler is a java process so you theoretically you could use it like that.
All our tooling is maven based, and today, eventhough maven has it's short commings, maven is the defacto standard it's supported by all IDEs.
Thanks for taking the time to summarize and post your findings, Malte! Clearly there are others who want to build Errai apps with Gradle, and I'm sure your effort will save them time!