Hi,
We have recently performed a similar migration to Android Studio across all of our Android codebases. All of our Android apps/libraries are now built with Gradle, both directly through Android Studio and as part of our Continuous Delivery processes.
I would be very happy to help you with moving towards Android Studio. You seem to have picked out the most important aspects (resolving dependencies etc.) of migrating to Gradle. After a quick look at the codebase, it appears there are no tests for the android messenger app, so I would assume making the app build-able with Gradle/Android Studio would be sufficient?
I have outlined some milestones, which should help you assess my bid.
Please don't hesitate to ask if you have any questions,
Phil