I know this sounds awkward, but in sentences such as "He said me being here was wonderful," it's obviously grammatically incorrect to say "me being here." It should be "my being" because we need to use it as a gerund and conform to the grammatical structure. But what about in the example of "If he had my doing (of) this from the beginning, we would have succeeded?" Because if you say, "If he had me do this from the beginning," there seems to be a conflict of "had" and "do" because both are verbs. Can someone explain, please?

For reference, I'd like to share this from <a href="http://afterdeadline.blogs.nytimes.com/2012/05/29/one-of-those-things-again/?_r=0">NY Times on Grammar</a>

"Aurélie Filipetti, 38, a novelist and a legislator, was named culture minister. She had made public an account of being groped by Dominique Strauss-Kahn, the man **whom** many thought would be the Socialist candidate." The correct answer here is "who" and not "whom" because the subject is doing the "would be" verb.