@Warsaw Will - thanks, that clears it up rather well! You're right. In any case, this is all hypothetical. There are far cleaner, less ambiguous ways of saying these things!

@ Warsaw Will - What about "I so appreciate you taking me and Gregg's child to school today"?
Now, I know that at first sight, it seems wrong - the "me" could come across as a 'dangling object', as if the addressee were taking two people to school: the speaker, and Gregg's child.
However, in speech, one would say, "Jack said Romeo and Juliet's love was eternal". It wouldn't be "Jack said Romeo's and Juliet's love was eternal". So, if we transfer this rule onto the original sentence, could it not be "me and Gregg's child", which sounds more natural despite risking the intrusion of a 'dangling object'?
(I am aware that in speaking, no-one would actually phrase it like this. But for the purpose of argument, let's say we had to, and we had to make it grammatically correct.)