We used a very similar model to this at my last job, and I'm struggling to get my current team on board with this type of process. I think the main problem is that people don't trust continuously deploying master because there aren't enough tests. In my ideal world, every commit is tested (with Jenkins, Travis, Buildbot, etc), and then if the PR includes tests for the code and the build passes, the reviewer says LGTM…
This isn't an unattainable utopia. It's what lots of teams are doing now. Try out continuous integration services (Travis or Koality).
And, given you have good instincts, ping me when you're looking for a new team ;)