For your routes... UA is probably the best avenue for you...
I disagree. Either AA or DL would be quite workable on those routes from LAX. Also, UA flies RJs on SEA-LAX and doesn't have great timing on those routes. AS flies big jets and many more flights (plus BUR nonstop service too).
To be honest, I think we need to know a bit more about the OP's potential travel patterns.
To the OP: will your employer be paying for business on the LAX-NRT/ICN flights? This has a bearing on the recommendation (whether you could be potentially stuck in coach for 10+ hour flights, whether you'll value E+ more or the ability to get OUT of coach on those long flights.)
Also, if you had to trade ability to upgrade domestic flights (including AS) (DL) for better ability to upgrade longhaul international flights (AA), which would you pick?
Also, if you HAD to take your business 100% to UA (in order to keep status) would that work for you? Or is having the ability to choose an AS flight important?
Making *A Gold and getting free lounge access and E+ on your intl flights is a nice feature of that program and if you hit 100k miles, the 4 SWUs are an unparalleled advantage.
If you could hit 1K on UA, you could hit EXP on AA, which nets 8 eVIPs good on ANY coach fare (not just pricey ones like on UA), and oneWorld Emerald, which gives you F lounge privileges (better than *A Gold). Most EXPs seem to have very, very high upgrade percentages (and you don't get free upgrades on UA on LAX-JFK as a 1K without using an instrument, but you do as an EXP on AA).
That being said, the OP hasn't indicated that they would hit 100,000 miles of flying annually, so it's possible we might be comparing UA 1P/DL Plat/AA Plat.