First, before you move them to the Independents, are you using the Practice Cards? Part of the power of the Independents is that they already will not like staying for 2-4 minutes to do rules practice, and so them getting a card because their friend did really bums them out and makes them want to get off the team. Also, they might have more respect for the Scoreboard once they start getting practice cards.
Try practice cards before you go to Independents if you haven't already. It's a loooooong year.
I did move much faster than the usual recommendations in that I ran Scoreboard Level 1 for about 2 weeks before introducing the Guff counter (because it was needed!), then introduced white practice cards after about a month, and that's lasted me through first quarter. I'm introducing purple practice cards start of second quarter because they're ready to start earning off their white cards by doing well, I feel. I started Independents about three weeks ago, two weeks after I introduced practice cards. It has been extremely powerful, but it's mostly powerful because the other pieces are in place.
Biffle put it really well at one of the conferences: We all focus on those problem kids at the beginning of the year and think, what can I do about that kid? How can I tackle his problems now and stop him from misbehaving? But that's not what the Scoreboard is about. The Scoreboard is RTI in and of itself, Level 1 will get almost all your kids, in this case it sounds like all but 2. Level 2 might take care of them, then Level 3 might get them if Level 2 doesn't, then Level 4, etc. The reason to not just start at Level 4 is that Level 1 takes the majority of your kids and puts them on your side. They're not just there and being good, they become your teaching assistants in keeping the other kids in line.
My students now will tell me to put someone on the Independents when they have been acting poorly and scoring me lots of points. They effectively ostracize the poorly behaving student. That sounds awful, but I can tell a kid day and night to tuck in his shirt, and he won't. The minute the other students start suggesting he get put on the Independents, he says, "I don't want to be on that team!" and stops. That only works because the other students have full buy-in on the Scoreboard, and the Practice Cards and Guff Counter are in full play.
So, you're asking what works with the worst of the worst kids? The exact same system, no changes, just a little accelerated.
Finally, are you rocking a Super Improvers wall? I have a 14 year old gang member who was arrested last week for shoving a teacher come in today because he went a whole week with no discipline issues because he wanted to put stars up on his Super Improvers wall. He is excellent for me.
It still blows my mind that this hard hood kid who has had guns put to his head several times is super stoked about drawing stars on a colored piece of paper for no reward, and that is more powerful than all of the Scoreboard levels in getting him to behave better.