I'm not sure where you're getting your $3.9m and $3.1m figures from, because Karlsson's cap hit is currently $10m. Half of that is $5m.
And in real cash, there may not be a lot left on his deal this year--about $1.5m--but next season he's owed $7.5m. $6m of which is owed in bonuses. And no, I don't believe you're correct. Chicago would be paying half of that bonus if the rule is consistent.
@Fourier might be able to weigh in.
Chicago alone would ask for a significant return just for multiple years of retention. Then you're paying Pittsburgh for the former Norris winning defenseman. It would absolutely run you two 1st rounders minimum.