In general I like this idea very much.
For the bulls, they r loaded at 1-2, think about it, Rose, Gordon, Duhon, Larry Hughs, Sefolosha. No way they would add Barbosa. Instead, they have been in need of post scoring all the years. Diaw plays his best inside, his scoring ability is very nice both face or back to basket, he's definitely a reliable double digit scorer if given consistent playing time, which he couldn't get here as backup after Amare and Marion. Bulls might think about it, as they r fire-selling Hinrich.
The main reason to trade away Diaw and Barbosa is to reduce payroll so that Sarvar could approve Kerr to spend full MLE on our first priority - a defensive and 3p shooting SF.
James Posey (let Shaq call him)
James Jones (he has already chosen not to pick up his player option and became unrestricted FA)
Pietrus (younger, better defence than JJ but less accurate 3p, rumors said the Spurs want him)
and a few more.
Diaw for Hinrich is about equal in salary (9M for 10M for this season), we got a strong backup PG, maybe more expensive than we'd like, but Diaw was expensive backup anyway. It is also possible to play Nash and Hinrich together.
Then, there is absolutely no need to keep Barbosa, we can trade him for a good SF at same salary level (6M) or just to clear cap space for FA signing. To New York for David Lee and for trade exception? Or, to Portland for one of their SFs?