Exactly. There's really no point in going after a player who has collected more bounty chips, because in the end, you either have them all or you have none. Going after the player with more bounty chips is a bad strategy in this type of tournament.
But in re-reading your post, it sounds more like this: each player gets $2 for each bounty chip they win, but when they are knocked out they must give all of their bounty chips to the hitman. However, they busted-out player gets to keep the money they won for the bounties they collected. And whatever is left in the pot goes to 1st place. That means that the bounty chips can compound, so you don't know beforehand how much money will be handed out due to bounties.
Examples:
(1): 10 players. Player A knocks out 4 players in succession. Player B knocks out 4 players in succession. So Player A and Player B have now collected $8 each in bounties. Player A knocks out player B and collects $8 more, for a total of $24 in bounties ($16 to player A and $8 to player B).
(2) 10 players. Player A knocks out all 9 players in succession and collects $18 in bounties, for a total of $18 in bounties.
(3) 10 players. Player B knocks out player A and collects $2. Player C knocks out player B and collects $4 in bounties. Player D knocks out player C and collects $6 in bounties. Continue until player J knocks out player I and collects $18. A total of $90 in bounties has been collected.
Is this the way you play?