I think it would be much easier to limit the carrots to physical objects only. Some careers might end up being more or less interesting, but that's part of our strategic choices. I don't feel this limitation would make the challenge less funny or interesting for me, for instance.
Some of the special abilities, so non physical potential carrots, are funny, but I think it might be very complicated/confusing to keep track of those for the multiplier without a list. And a list would ruin part of the challenge maybe.