After reading your posts, I see that you believe either case is correct, and you put forth a strong argument. If I were to use the possessive case with gerunds, however, I firstly need to know if a verbal in a sentence is in fact a gerund or a participle.
Generally, distinguishing between the two non finite verbs is easy, as gerunds take the place of a noun (appositive, subj, object, etc) and participles function adjectivally modifying a noun.
With the two sentences I provided above, could you please talk me through how you determined why they were gerunds. Personally, I determined that they were gerunds by realising they were both objects of the verbs proceeding them, but if you have another way to distinguish them, could you please share this with me.
Additionally, since you seem to know quite a lot about this, can you read over my post on the following discussion (scroll down once you're there). No one seems to know the answer.

The discussion is on the uses/types of ing phrases (free modifiers).
http://www.englishforums.com/English/Participle/vmcp/post.htmThanks a load!!