1maniac,
I'm not a real big fan of what manuals specify any more. I used to be, but changed my mind when I discovered that my Euro car was getting heavier oil everywhere but here in the US. From what I understand, several German car manufacturers are now spec'ing xW-60 wt oils for their machinery. Europe has just as much temperature variation as the US, but more costly resources. To me, this says volumes.
I've never owned a BMW, but keeping in mind that most US manuals will spec a thinner oil than their non-US counterpart, I think the fact that your manual DOES say 20W-50 means something. My guess is, for that engine, BMW is more concerned about the 50-end than they are the 20W-end.
If it were my car, I'd continue to use what you're using right now: M1 15W-50. It's advertised as having more anti-wear additives than the other M1s, & it's going to do its job well outside of any extremes you'll see. Since you've got the Amsoil on hand, I'm sure the 20W-50 will perform at least as well as the M1 15W-50. I'd save the 10W-40 for another engine. No, I don't think you'd have ANY problems running it, I'm just saying if it were my car...
For reference, I'm running M1 15W-50 in a weakling 125hp 4cyl in CO, & I haven't had any cold engine problems yet (down to 15*F so far this year!).