Basically I am adding on to ThumbsUpMaster's theory:
http://www.youtube.com/watch?v=gKeT0cjYB5U&NR=1
I think that's pretty spot-on. Here's how I see it:
Stop 'N' Swop was first planned to utilize the N64's extra memory by copying the text that the Stop 'N' Swop items held in Banjo-Kazooie, into the system's extra memory (when the items were activated).
Then the text from Banjo-Kazooie would activate the Stop 'N' Swop eggs and ice key in Banjo-Tooie, through a now canceled feature (possibly in the tower room, like ThumbsUpMaster stated), which would just be the six items ThumbsUpMaster noted in his theory.
Then, I believe a while before Banjo-Kazooie was released, Nintendo decided to can the N64's extra memory, leaving a huge gap in Stop 'N' Swop's original plan. Rare would have to find some other source of memory to copy the text into so it could be copied into Banjo-Tooie.
Still in the beta stages of Banjo-Kazooie-possibly somewhat soon after the N64's extra memory got canned-a couple of beta Donkey Kong 64 and Banjo-Kazooie screenshots came out that included cameos of each others' games, seemingly linking the two together:
http://www.rarewitchproject.com/?id=1274
Which is interesting, considering Donkey Kong 64 was one of the few games that actually utilized the expansion pak (and I believe it was one of the first).
More recently, the RWP found the text "Ice Key" in Donkey Kong 64 (for reference, see last link). Some believe this to be merely for testing, which would make sense, considering that I think Rare was messing around with their new form of swapping, and wanted to test it, but if those cameos really did link the games together, then why would Rare go to all that trouble to change in game features-and then release them to the media-just for testing that was never going to be released to the public? If those cameos weren't a connection between games, then why would Rare go to all the trouble to take them out and replace them?
Anyways, I think the feature then got dropped due to various reasons, such as the thought of marketing a standalone device-and/or possibly three games-just for some in game prizes and a sequel that otherwise wouldn't require a standalone device (considering the original plan was to use the N64's extra memory, which wouldn't require any extra devices, it wouldn't have required any additional costs).
Instead, Rare decided to just try to cover up the original Stop 'N' Swop plan and replace it with the same items it would have given, just in-game.
So my main questions about Stop 'N' Swop really have to do with what it's original purpose in Donkey Kong 64 was suppose to be and what the original procedures you had to do in Banjo-Tooie were. Aside from that, I really think that's all Stop 'N' Swop was.
There's only one other interesting thought I can think of at the moment, and that's that maybe the items mentioned in ThumbsUpMaster's theory were originally planned to serve purposes..