Sorry for being confusing.
I have an item I want on my game when I start over for the challenge. Just trade me 2 dud pokemon for my 2 Pokemon, and take the items off them (You can keep one). I will then start the game again, get the starter yada yada, until I get the Pokeballs and catch some dud pokemon.
You will then trade me the eggs for my dud pokemon. Also, you would trade a dud Pokemon holding the item I want for another of my dud Pokemon.
Does that make any more sense?