I will never turn down the first overall pick, but getting a max free agent (of the Hayward and Griffin vintage) just became much more difficult.
If we let all the free agents/non-guaranteed guys go, dump Jackson, and convince Yab to stay overseas another year, we're at $28.8 million cap space, $1.5 million short of a max. Even also moving Rozier would not create enough room.
If we instead keep Olynyk and trade Bradley (along with everyone else described above), they're at $29.9 million cap room, still about $400k short. Moving Rozier in addition would work, but if you want a max player, get ready for some sort of significant trade.
Not according to my math:
Player 2017-2018
1 Bradley, Avery $8,808,989
2 Brown, Jaylen $4,956,480
3 Crowder, Jae $6,796,117
4 Horford, Al $27,734,405
5 Rozier, Terry $1,988,520
6 Smart, Marcus $4,538,020
7 Thomas, Isaiah $6,261,395
8 Top Pick $7,026,240
9 Max FA $30,300,000
10 Zizic $1,645,200
11 Nader $815,615
12 2nd rounder
$815,615 $101,686,596 Replace Rozier with a $816K player and you're under the cap. Assumes everything you do including keeping Yabu overseas (probably should), dumping Jackson with a pick, and dumping KO, TZ, and JM. You might well get decent pick value back for Rozier.
I think you forgot to get rid of one of the minimum players when you figured the max room available to sign your max FA as the twelveth player under the CBA.