Big head mode as a cheat code is a must, it's just too much of a thing I think of when it comes to Rare type games. Maybe cheat codes could be unlocked with something similar to what jiggies are? (Just as a throwback to Banjo Kazooie) Like maybe... ripped page pieces that can be put together by some NPC character that uses magic to fuse them, and once done they reveal the code (And the code would be placed in a menu/library of pieces of papers with the codes followed by descriptions).
Even better, it'd be a small feature, but giving no description to an unlocked cheatcode until you use it would be fun too maybe (though I can see that being a negative thing so maybe not).
As far as other things go, yes, a dryer machine would be amazing to have haha, or even better, something that goes right back to the roots, an ant. Hrm, or something equivalent, like a... beetle maybe?
Other throwbacks to Banjo Kazooie would be great though I don't know how far they'd be allowed to go. Other rare game cheat code references would be nice too, like the game's currency/coins could have a code that gives them eyes and makes them bounce away from you (Conker). Maybe a cheat code that makes your character pull out a ukulele and play it as an attack that kills all enemies around you (Donkey Kong 64. A code that gives you're character a golden slingshot (or the equivalent of a projectile weapon in the game) would be cool too.
Aside from that, cheats can kinda depend on the games content too, who knows what's possible. You've basically listed all the basic cheats I could think of
so that's pretty covered.