Pretty good timing on this post. I just started working up loads in my 1903 using Barnes 120gr TTSX's last week. As mentioned, different rifles seem to feed differently but they feed well in mine as long as I seat them as long as possible (still fit in the magazine) and run the bolt hard. From memory there is a raised portion on the follower that begins right in front of the case shoulder. When the cartridge is pushed forward the tip of the bullet lifts the cartridge over this lip. Since the pointy bullets are narrower at the tip there is less lifting action than a wider round nose has. Hence why I need to run the bolt. If I try to close the bolt like a brit holds his tea cup it hangs up.
I don't think you could go any lighter than a 120 and still have enough length to do this.

So far accuracy has been good but I just got the rifle and have not compared it to a 160 cup and core round nose, or anything else for that matter.
I've only used StaBall 6.5 and H4350 and it looks like 2700fps out of my 26" barrel will be easy. I may even get 2800 or more. Should be a real killer with the TSX and has a far better BC than the heavier round noses.