60hz 3D is 120hz in the projector. 60hz left plus 60hz right equals 120hz. Even if your computer could handle 120hz 3D (240 fps, yikes!) you're limited by what the projector can do, and more specifically, what HDMI 1.4 can handle. 3DTV Play has those limits because it's the best HDMI can do. That's my understanding anyway. (EDIT: I'm being sloppy with hz vs fps here. You can show a 24fps movie at 60hz, for example. Just wanted to acknowledge that.)
In any case, I doubt the fresh rate is the cause of your eye strain. When you're playing games, turning down the intensity of the 3D would probably help. If you're new to 3D or haven't viewed it much recently, you might just need a little time for your eyes to adapt to it. I had quite a bit of eye strain when I first started viewing 3D, but after a few days it went away without changing anything with the display or the 3D intensity of games. Now 3D is completely comfortable for me.