Check out the Remington 180 Core-Lokt {single-cannelure}. In my tests it has performed superbly at .303 velocities, expanding and holding together well and producing pretty classic mushrooms and good penetration. If you care to compare some bullets, see those tests here:

http://forums.nitroexpress.com/showflat....d666b4835845898

These bullets are inexpensive and in my opinion the best overall .303 bullet for deer/elk/black bear. I cannot see any good reason to set a .303 up with 215's currently due to variable supply and bullet cost and frankly, cannot imagine what advantage a "Premium", expensive bullet like the Woodleigh or some other custom bullet would offer in .303 on the game you identify unless you don't care about cost or don't plan to shoot the rifle a whole bunch.

Remington 180 .303's have one slightly odd characteristic; they are slightly undersize {at least all lots I've miked or have read others measure are} and go .3105. Not a real problem, but merely an observation. I did have one set of dies that did not provide adequate neck tension with them, and had to grind the expander down.

If I was going to have a custom .303 set up {double or otherwise} with fixed sights, I'd have it zeroed for the Remington.

Just my $.02.