OK what about this trade:
Chicago trades Noah, Boozer, Hinrich and Hamilton for KG, Paul Pierce, Bass, Lee, Randolph and first rounder (2014).
Bulls would then compete with
Rose, Teague, Lee, Crawford, Butler, Pierce, Deng, Gibson, Bass, KG and Randolph
Pierce and Deng expire while KG will probably retire leaving them with tons of cap space (around 20 mil), prospects (Butler, Teague, Mirotic) and picks (3 first rounders in next years loaded draft) to build around Rose. Pierce and KG might agree to go to Chicago for a final chance to contend and play for Thibs.
Boston picks up Noah to add to their core and bites Boozers contract at the cost of a first round pick.
Rondo/Hinrich
Bradley/Terry
Green/Hamilton
Boozer/Sullinger
Noah/Melo