After further research on the me/my use, it is not as clear cut as you seem to make it. Apparently some guru named Fowler would have disapproved, but the use has been more common as time goes on since Fowler. It would also be more common in informal speech.
"It is correct to use the possessive adjective (my, your, his, her, its, our, their, Mary's, etc.) with the gerund, which is, after all, a noun, the noun form of a verb. However, when you are speaking ? perhaps with people who don't use possessive adjectives before gerunds ? you might feel too correct and uncomfortable to use them. The alternative form, for informal use, is to use the object pronoun (me, you, him, her, us, them) or Mary, John, etc., before the gerund.
Several grammar texts, including Practical English Usage by Michael Swan and Understanding and Using English Grammar by Betty Azar, note this distinction." Mikek