I think it should be Team because the attack was aimed at all of you, even if it didn't even come close to Hercules. Sleeper isn't "on his own" anymore.
Also, while I didn't say anything before, I'm not sold on that justification for Spawn of Venom. I wouldn't give Spider-Man bonus dice fighting Mysterio just for having fought him before, and that would be firsthand. If you were exploiting something secret, then that might be different.
But yes, you are correct that the stress is "permanent" and both you and Kaine can exploit it.