Ah! Another Mystery Gift enthusiast! It's a miracle!
My "Stadium 2 loot determined by your own OT" theory is mostly out the window now. Another one of my saves received a Magikarp Doll from Carrie and there wasn't any out of the ordinary loot the previous day, so I don't think there's a special trigger there anymore. I do still feel like there's some funkiness going on, though. All of the rarer decorations I've received from Carrie (that I'm aware of) were decorations that those saves themselves were able to distribute. I'm not sure what to make of that. Have you received any rares from her? Did they match what your OT is able to distribute?
Regarding Carrie frequently mentioning the TENTACOOL DOLL, I'm not certain, but I think she might stick with the same rumor until you break your gifting streak. Also, I think there's only rumor dialogue for TENTACOOL DOLL and PIKACHU BED (no UNOWN DOLL). Sort of weird. If there's a special trigger for the uniques, I'm thinking maybe it's related to Carrie's own decoration collection.
Documentation-wise, besides the aforementioned Reverse Engineering of IR Protocol thread, there's an incomplete and inactive disassembly of Stadium 2. That's pretty much entirely over my head, though.