It seems that the concept of "Pull Requests" and the concept of "Code Reviews" are actually two separate things -- or they can be, depending on how a team works. It makes sense to have two separate options, "Open new Pull Request" and "Open new Code Review", where the differences are:
1) a "Pull Request" can't be opened if there are conflicts in the merge, and
2) a "Code Review" can't be automatically merged (i.e, the big green "Merge" button would never show up).
These should be able to share a significant amount of the same backend implementation.