Let's say JuJuan Johnson and Jeff Green are signed to a combined $10 million. That would mean $38.6 million for 5 players. That puts them 7 players below 12. The cap space would be further constricted by 7 times the rookie minimum salary, which will be around $3.5 million. The stretch rule won't matter because you're not really going to cut Pierce or Rondo.
So, they would have about 58-38.6-3.5 or $15.9 million. But you also have to subtract the rookie scale contracts of any first round pick, which won't matter if those are used to acquire a max contract.
If you trade Bradley for a future pick and also trade the first round picks, then you have a team of Rondo, Pierce, Green, Johnson, your max free agent, whoever you can sign for that mini exception for teams that start out under the cap and go over it, and a bunch of minimum salary guys.