So I thought about what one of the most important things is to him currently and came up with computer time. Right at the end of summer vacation, he started to show a noticeably increased interest in playing online games. So instead of punishing him by taking this away, we decided he can earn computer time in 15 minute increments by being a good big brother. This includes being nice to the twins, helping them out without being asked, playing with them when they ask even if he would rather be doing something else, among other things.
I created these basic computer time coupons below to make this positive reinforcement more official (and fun). He can collect them and cash them in anytime when computer play is appropriate. I thought I would share them in case they might be useful for your household.