you can find long connections on ua very easily, probably not defined as a stop but i sometimes like having 20 hours in ord or something

saa's business is not very good, i'd do what others are suggesting and go the lh or lx route out of lax. i would not pay for sa business, it's really mediocre.

be careful with that sa jfk flight, every so often the flight sked reverts to a different equipment which makes a stop over in dkr or acc. used to be during northern summer only, then northern winter, then ???. so keep track of that. the stop over is annoying and saa is a really irritating airline to fly with (you can't have blankets on during takeoff or landing, they play the same repetitive announcements, same slow service, etc).

also there's turkish airlines which i love flying on, i know they fly out of sfo and iah for cheap. and i'm pretty sure you can get a stopover on a business ticket. also you have long connections in istanbul so you can wander out if you're keen enough.

for schedule especially out of san ba is hard to beat.