So, how are we gonna do this?
I've been trying to think, but we might have to kind of ... shuffle the character deck. The problems I keep running up against are as follows;
1) Joker's only interest is clashing with Batman, and nothing makes him do anything else.
2) Depending on the publication, Ivy's motivations are limited to destroying all of humanity, and being Harley's girlfriend/kind of maybe empathizing with those stupid humans.
3) Deadshot is in prison, if he isn't in prison, he's retired, and the only reason he picks up his gun-gauntlet thing is because Waller is threatening his daughter. Daughter this, daughter that.
Harley is fine ... she's a super dynamic character in terms of her development over the years
So, Deadshot works for a by-the-books Suicide Squad plot, but Joker and Ivy don't. Joker could be more workable as an anti-hero if Batman has disappeared. In the past, he's become a very ... not great hero in an attempt to cope with his nemesis being gone. Deadshot's daughter could easily be threatened again, and Ivy could be at the point in her development where her love for Harley has reawakened some of her empathy for humanity.