Like Sled, my wife has a preference for me to shoot non-lead bullets out of my 270 Win. I currently use the Barnes TTSX 130 gr and I like them. The one caution I would add about these is to pay attention to your impact velocity to ensure sufficient expansion. Barnes says these expand down to 1600 fps, but I tend to be conservative on that and prefer 1800-1900 fps. That puts my own personal limit on these bullets at around 500 yards for deer and about 400 yards for elk. In reality, I have never pulled the trigger on any game beyond 325 yards, which is my current longest shot with a non-lead bullet. That bullet opened up to the base of the cavity, broke a shoulder, three ribs and then traversed the length of a pronghorn, coming to rest under the skin behind offside hind quarter. It wasn't the best shot to take for a dirty meat hunter like me. But aside from the front shoulder, the damage to the meat wasn't too bad. I've got a lot of faith in these bullets as long as you don't stretch it too far. I've read that the Barnes LRX bullets have a higher BC and are built to open at slightly lower velocities than the TTSX, but I would not trust what I read without some personal testing. If you really want a bullet that stretches your range, I would stay away from non-lead in favor of a bonded lead bullet or a partition.
I would also echo what Charon says above. Shot selection and shot placement are key with a 270. Pick your shots to avoid the big bones. Put it in the boiler room at a distance where the bullet will open up and it'll do its job.
Good luck.
