App Engine expects your web apps to return almost immediately (in a matter of few ms). For anything that takes longer, you need to use task queues in App Engine. Or maybe try AppEngine Managed VM's?
https://cloud.google.com/appengine/articles/deadlineexceeded...
(I work at Google, but not on App Engine)
https://cloud.google.com/appengine/docs/java/modules/#Java_I...
If you run multiple modules at once (some serving the frontend, some for longer tasks w/task queues), you can have the best of both worlds and use different scaling options for each.
(I also work at Google, but also not on App Engine)