To the woman who is going through something similar with missing cards from an opened envelope, this should give you an indication of how Target will handle your case. It's sad, but I will not be surprised if Target says tough luck.
I feel like I should point out that the fault here does not lie with Target. Target did not choose to save on shipping by offering Mail Innovations. You (or me...the customer) chose to save on shipping by selecting the free option. Mail Innovations does not offer insurance. Think of it as "you get what you pay for", which is nothing. It's bare bones shipping with tracking and nothing else. That's why it's free. Point is that Target isn't to blame if you decide to choose to save money on shipping.
This is most likely true. You have to remember these gift cards are shipped like everything else from a giant warehouse. They are probably all activated already and ready to be shipped. It cuts down on time and manual labor in a warehouse that I assume is all or mostly automated. The packing slip shows the carton, box code and chute numbers, which tells me that these are all together just waiting to be shipped. Punch in the item, wait for it to arrive and then pack it up.
Like I mentioned above, if they arrive at Target activated, there is no way to get an individual activation number. Disney won't be able to help because the packing slip from Target just includes the item #, the DPCI #, description, and general UPC #. Everyone who orders has the same information, there is nothing unique to differentiate your cards from anyone else's on the packing slip.