From the video it appears (four teeth turn) you have an interference 3.0L. Is that correct?

Having the cams snap forward at about TDC is a problem on my engine as well. I found to let it snap past TDC then turn the cam backwards, CCW to TDC and it should hold. You can turn the cams and the crank CCW as long as the belt is not installed.

Once you have TDC I'd get a helper to get the belt on - wife bonding works.

92 Montero LS 3.0L V6 Auto, Stock, Original owner, 185,800K miles