I don't think LA's fate has much of an impact on an assessment of the trade. I think, and have always thought, that the key to our defense is defending the paint. That's the case whether we're defending it against post scorers like Gasol and Randolph, or from penetrating guys like Lebron, Wade, Rose, etc.
Now, if Green focuses on defense and energy and provides timely scoring, then I think he can offset some of what Perk brings. However, I'd still feel better with Perk in the middle, giving us 48 strong minutes at the center position along with JO and Shaq.
And who do you have playing in place of Green's minutes, or backing up Paul ? Sasha ?
Right now, Perks having trouble moving on help defense. He's flat out slow and lethargic. If he is late on Wade or Lebron, or on any type of ball movement, I see 3 easy fouls in 7 minutes on him. Boom he's out.
Then what ?
I'd rather have the roster we have now.
As has been stated, oh, 63,000 times or so, I think we would have pulled off a smaller trade for a swingman, whether that be Anthony Parker, Corey Brewer, Rasual Butler, Jamario Moon, or somebody else. It's not like Jeff Green has been a world beater in the playoffs, so it wouldn't have been hard for somebody else to approximate his contribution.
I do, however, hope Green plays better. Game 3 was a step in the right direction.
As for Perk's lateral movement, I'm pretty sure it's better than Shaq's. 
Same could be said for Perkins. " It's not like Perk has been a world beater in the playoffs, so it wouldn't have been hard for somebody else to approximate his contribution "
What has Perkins played, 2 good games in the playoffs so far ? Maybe not even that ?
I think I'll take the roster now, plus the future options instead. Perk himself before last game confirmed he's at 65 %, and thats the Left Knee, not Right. So, Shaq or not, he's not near 100 %.
He's got issues moving right now, and that doesn't bode well against playoff teams that move the ball, or against teams with guards (Wade/Bron) or Forwards who can get to the hole. Thats foul trouble at its best, especially a player like Perkins.