Re: negative clause + affirmative tag
Politeness is more important than logic.
If I say "You could carry this for me" I'm assuming you can and will and want to.
If I say "You couldn't possibly... " then I'm assuming that I am too much trouble and then YOU say that of course you can. It allows the other person to take the lead on doing the favor instead of my assuming he will do it. (I don't assume anything - it's just how the dance goes.)
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.