We've had good success with trading time limited computer access for behavioral goals. We've had a problem however when the time is up. It's very hard to stop, especially during a game.
I'm sympathetic, but with this sort of thing our son does better with firm boundaries. On the other hand, this has led to some difficult battles. As the #1 son moves further into adolescence, it's harder for Mom to enforce rules.
Still, this is a battle worth fighting. Tracking time, recognizing a deadline, then overriding the desire to continue are great executive function exercises. It's push-ups for his frontal lobe.
Recently I've had some success with flipping the problem around. As well as punishing him for going past his time limits, I'm rewarding him for finishing early. He gets to rollover unused minutes, and he gets three stickers (8 stickers = 10 minutes computer time) if he finishes before the timer completes*.
This has worked better than expected. We remind him prior to logging him in, and we remind him about about 4 minutes before the end. He's getting good at ending 1 minute early (or a bit less, since he knows we round up. There are times I wonder about how accurate his IQ testing is.)
Eventually, if he continues to succeed, we'll dial back on the reward but he'll always be allowed to rollover unused time.
It's surprisingly hard for us to come up with these judo moves; it's easy to get stuck in a pattern of confrontation. When they work though, it's satisfying.
* We use a visual timer that has become popular in the special needs population.