It's an interesting corner case. I believe it's "I will look at whomever Bob greets." (as you note) and "I will look at whoever greets Bob." The object of th

It's an interesting corner case. I believe it's "I will look at whomever Bob greets." (as you note) and "I will look at whoever greets Bob." The object of the preposition is the phrase "whoever greets Bob," so subject-to-a-verb wins.