Thank you all for your comments. Because of my dad's age (and lack of English), I need to keep the number of connections to a minimal. Having him try to find the right gates in multi-terminal airports like JFK would be a nightmare... Otherwise, I have a lot of skypeso to work with... (KE via ICN has decent availability if I only need 1 ticket in coach).

I spent over 2 hours (combined) clicking away looking for availability on aa.com over the last few months. I wish I knew sooner that I cannot find partner flights... I did call once (before Christmas) and they told me no availability either.... I do notice that last minute availability on the flights I want (YYZ-HKG) do show up ~2-5 days out. So I am hopeful. I will continue to check ba.com for availability, but book by calling AA.