If you want a short barreled magnum, go with WSM. You'll get more speed out of that than the win mag, since the win mag takes longer to burn the powder. That's why it's common to see 22 and 24" WSM barrels, and 300 win mag is most common on 26" barrels. The WSM works better with faster burning powders anyways, so if I had to guess you'd get at least 75 FPS better on the WSM than on a 20" win mag. I'm just speculating there, but there's a reason there's almost no 20" win mags.
30-06 is also an option and would probably not even be too far behind in velocity from the win mag at such a short barrel length. But if you insist on magnum, 30WSM all the way.
edit:Youre asking a lot there for "must have long barrel life, cheap ammo, power for 1000 yards, widely available, work with a 20 inch barrel for both hunting and 1000 yard shooting, etc"
We need to all learn that nothing will ever be perfect and you'll always sacrifice on something. If you're wanting to go out to 1000 and do all of those things you're either going to have to sacrifice barrel life, ammo cost, or start to reload yourself. Factory win mag ammo is designed for 20 inch barrels and you're just wasting powder and not getting the most out of it. I stick by my 30WSM recommendation, but the ammo is a tad more expensive than you're asking. But nothing is perfect, choose a sacrifice.