Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
If your primary concern is minimizing out-of-pocket costs, you might consider transferring MR points to Air Canada's Aeroplan program, and then redeeming for LAX-NRT on United. I believe that Aeroplan does not (currently) assess any fuel surcharges for redemptions on UA metal.
Of course, you should not transfer points to any program before determining that there are award seats available on your desired dates of travel.