If a 180 gr in '06 is considered sufficient for big bears, why wouldn't a 200 gr .323" at 2600 also work? I'd think that you could get better velocities from a slower powder like Big Game perhaps? Here is what their manual lists:
Big Game 200 NOS A-BOND 45.0 2,330 50.0 2,550 54,000 3.115
When I picked up a .325 WSM I was told by several people that the 195 gr Interlock is a really tough bullet and a great length for an 8x57. Also, if you look at the rating on the 180 gr NBT it is built pretty tough as well, plenty for elk, but bears I'd do as you're looking to w/ a heavier bullet.
The 220 Sierra is REALLY long and built for the 8 RM so unless you have a super long throat I wouldn't think you'd get enough umph behind it to make it expand fully, although the Hodgdon site suggests you can get about 2400 w/ H 4895. That'd be a heckofa thumper!
Good luck! I'd love to hear about your results. This is a severely under rated cartridge and I think it'd be great for the applications you're seeking.
