Gay certainly seems like a good fit. In past years recently signed players could not be traded until after a certain date. Idk if that rule still exists or if that date has passed, but it could hamper Chicago's ability to trade players. One of the most difficult things about NBA trades is making the salaries match. Gay makes $13.6 million, and it would be difficult to trade him. I would also be surprised to see Memphis try to move him after just resigning him.
Hamilton ($11 mil) could become available, but he may not have much left. I really like him as a player and think he would be a good short-term fit. His contract may make a trade difficult as well. Brewer, Korver, Asik would be close to matching salaries.
As for the 2-3 years, the Bulls don't have the players or maturity level to contend this year. Even if they were to pull off a miracle and add Melo, they would still likely be behind LAL, SA, and BOS. Those teams all look to be worse in 2-3 years and that could be the season for CHI to load up. MIA and OKC (NY?) are the other teams that should contend well then. A lot can happen in 2-3 years...
FYI according to Hoopshype.com, the Bulls have $56 MIL in contracts this year with a $58 MIL cap. Kurt Thomas and Scalabrine are the only 2 expiring contracts this year with totals of approx $2.5 MIL.
http://hoopshype.com/salaries/chicago.htm