"the arrows 'seem' to fly straight but they are always slightly angled into the target."
Yep, I was watching a fellow shooting bare shafts into the gold at 90 meters, none of them "stuck" in the target straight nor did they appear to "fly" straight in the air...Did he have a tuning problem?
"My first thought is that the shaft needs to be stiffer. But shorten the shaft or decreasing the tip weight dosen't seem to make a difference. So I am wondering if the problem is me."
Yes, it's you, and me, and everone one else out there. Shooting a shaft "straight" is not an indication of good nor is it an indication of bad tuning. Use the planning method and end the frustration!
.....O.L.