Using a visual git client greatly helps with this approach, especially if you are coding in multiple files at once. Once you have "green" status, look over the changed lines in the git GUI and look for lack of patterns, code smells, etc. This separates the coder in you from the reviewer in you.
Perhaps I'm misunderstand you, but what difference do you see for this use case between visual and command-line git clients? I do this all the time with git-diff on the command line, and it might just be a failure of my imagination, but I can't think of how the process would be any different with a visual client. Can you give an example?
Different strokes. I'm like you: I do a git status from the CLI for peace of mind. Others in my company gotta have their SourceTree, and hate the CLI. I disagree, but it's their choice.