Presuming we come away from the lottery with the #1 pick which we will use on Fultz, in order to give Hayward the max we are going to have to clear an additional ~$3mil in cap space on top of renouncing all of our free agents (according to a CB article from a few weeks ago).
Swapping Jackson, Bradley and Crowder for Nik Vucevic and the 25th pick should do the trick. Then use the pick on Caleb Swanigan. I know a lot of people don't like Vuc, but you aren't bringing him in to be a star. He's an elite rebounder, and Swanigan has the potential to be a high level rebounder as well. On top of that, both are more than competent offensively. If you look at the end roster, we have addressed our 2 main weaknesses - scoring help and rebounding.
IT / Rozier
Fultz / Smart (or flip flop Smart to be the starter)
Hayward / Brown
Horford / Swanigan
Vucevic / Zizic
You can do whatever you want with the wing rotation (start Hayward & Brown, if you prefer). Either way, we have balance across the lineup. Much better scoring options and significantly better rebounders. You can complain about footspeed in the post when it comes to switching ball screens, but are Vuc and Swanigan measurably slower than the guys they are replacing (Johnson & Zeller)? And if you think so (I don't), is the small difference in footspeed worth the rebounding and offensive efficiency we would gain? You can still go small ball when desired, with Hayward at the 4.
For deep bench, you have your choice of Yabusele, Nader, 3 second rounders this year (less likely to have that many rookies on the roster) and vet minimum guys. You could possibly even bring back a guy like JJ, Amir or Zeller if they would agree to deals that would work within the cap. That would save you from relying on rookies for significant post minutes.
In no way am I arguing that this creates a team with no weaknesses, but I think it's much more equipped for playoff success than this year's roster, plus it provides balance across positions and across skill sets.