I am going to go with the assumption we look at Durant and kick the tires on Cousins and the rest of the usual suspects and decide the price is too high or we just get rejected by them or the rest of the NBA.
If we strike out on the superstars, these are some guys I think address our needs and are free agents, restricted free agents we could possibly pry loose or guys who are underutilized we could maybe trade to get.
Our needs are, in my opinion and in this order, shooting, rebounding (especially if we let Sully walk, which I think we should), and rim protection.
The free agent god of shot blocking and rebounding is obviously Hassan Whiteside. His blocks per 48 (6.1) practically laps the field with Jordan 2nd at (3.3.) There are however some surprising other players who are high in blks per 48 and are free agents also. Pau Gasol as 4th in the league in blks per 48 at 3.1. He also rebounds at about the same clip as Dwight Howard. Meanwhile he actually hits free throws at barely under 80% and has a decent post up and face up game. He even gets almost 7 assists per 48. He seems like the guy I'd call first at midnight like Danny did with IT. Durant's phone will be busy so why not try for Pau on a one year good money deal?
Also, 5th in blks per 48, Jerami Grant. His rebounding stats are putrid though but maybe Okafor and Noel were gobbling up the easy defensive rebounds. Grant does show up on the offensive boards.
Al Horford also shocked me showing up at 13th in blks per 48. In fact, looking at his overall stats, I was astounded by how little credit I gave him for being good to very good at... well pretty much everything. His rebounding numbers are low but to me you have to look at his defensive rebounding instead of combined because he isn't a guy who plays on offense in the paint. He was 32nd in defensive rebs per 48 last year.
As for shooting. Chandler Parsons and Omri Casspi, 9th and 12th respectively in 3pt%. Both tall, reasonably athletic, can switch to cover bigs, but decent enough to cover smaller guys and can really space the floor at the 3 and 4. If out there with Olynyk, IT could have another all star year driving and kicking it out to 9th, 12th, 14th (Olynyk), and 57 (Bradley.) Add Murray or Hield at the 2 instead of Bradley and it could be a great year. Al Horford was actually a better 3pt% shooter than Jae Crowder last year, 34.4% to 33.6%. Incidentally, Parsons also has a really good adjusted rebounding percentage which basically doesn't count off for balls that aren't near you or you defer to a teammate. That might raise his value more than maybe you'd think.
In summary, I think Horford and Parsons might hold the most value. Whiteside is great at blocking shots yet his dfg% isn't really high. That stat seems pretty iffy though and team defense might impact it as much as the individual. Horford rebounds well as does Parsons, so a combo of Horford, Olynyk, Parsons, and Crowder could offer some defense, rebounding, shooting, and overall be a pretty serviceable front line. Maybe Casspi could offer additional shooting and a trade for someone I wanted last year in Withey could offer a bit stiffer defense as his dfg% was outstanding. He just needs some playing time he isn't getting behind Gobert and Favors.
If Horford isn't available, or if he is and we are letting Amir go, Pau would be a great off the bench or limited minutes option at what would at least be a shorter contract if not a lesser money one.