You say...

He doesn't really want the children, he just wants to win.

You're absolutely right there. It can be a God send to recognize that this type of litigator is as his best in the limelight of the courts. They relish the attention.

My own now-X step daughter handled the situation with her NPD disordered X this way. When he went into the mediation session, the abuser strutted around demanding to see the kids every other weekend, all long weekends, one month in the summer etc etc. It amounted to about 25% of the time. In real life, he sees the kids less than 5% of the time and dropping. This NPD got what he wanted - to look good. HIs divorcing wife agreed to his demands, saying "You can see the kids whenever you want." Of course, he didn't want it at all. He only wanted to shine and she knew that and did that 'feed the beast' that can be a winning strategy.

Here's another strategy here, (scroll down a bit at this page)

See "visitation;
http://survivorquotes.bravehost.com/tips.html

Good luck!!