Barrett is really not my style (last name trendy) and it means "quarrelsome." Eeeek.
I like a lot of your middle name choices: Mannes, Willard, James, Robert, and Russell are all awesome.
What about Benjamin, Emmett, Owen, or Henry for first names?
But, if you stick with Barrett, I like Barrett Mannes and Barrett Willard. I like more random middle names!