I assume YYZ-UVF is simply for distance? If so, I would be a little cautious in case AA changes the flight numbers, in which case you'd end up with 17 segments.

Have you discounted DFW-ANC (though it's seasonal and service doesn't start until June 11, so it may not fit your plans)?

At the end, LHR-SIN-NRT-HKG-ICN is more miles but perhaps doesn't work as well for tier points?