Replying to myself:

I found the calculator at Traveldealz and did a bit more reading. It looks like,

• Malaysian would be the easiest way to obtain Sapphire, but not a great programme otherwise, so doesn't seem worth it.
• Qatar requires the least travel to obtain Sapphire just from cash fares, and would be the best option for shorthaul tier point runs; but Alaska has the points for award flights and BA will supposedly offer tier points through Amex, which would probably make them easier to obtain overall.
• Qatar counts all flight within the last 12 months, it's not on a "calendar year" basis or similar. And the lower target for retaining status would be handy.
• On the off-chance I land up flying much more than I'm anticipating, BA would be much tougher to get to Emerald than the others.
• There would be upsides and downsides to having miles in Alaska as well as Avios - more routing options and often lower fees, but another scheme to keep track of, likely meaning more money to be tied up in points in total.

Based on the above, it seems like it's between Qatar and Alaska; but the perks of Qatar (Better Doha lounge access and QCredits; plus no restrictions on lounge access within the US) seem to make that the right choice for me. Any advances?

Thanks!