Re: Sword tip movement
A few years ago Kondo sensei (of Daito-ryu) told a few of us that one of the highest forms of aiki is being able to cut straight. He told us to study it over and over again. He also did not explain much more and left it at that... His English wasn't good enough and our Japanese wasn't good enough and we had no one to translate.
In Shinkage-ryu we spend a great deal of time practicing straight cuts. In fact the first set of kata called Hojo is almost exclusively straight cuts. One thing we work on is keeping our hips square to the opponent. If your hips aren't square (belly button or belt knot facing straight ahead) you'll likely pull your straight cut slightly gyaku or jun.
Another thing I've seen is people not used to swinging swords is they tend to have a weak grip in one or both hands. This can lead to poor cuts. You might just need to strengthen your grip some with more suburi. Something that I like doing is sledge hammer levering. Do that for a few weeks and even a Shinkage-ryu bokuto will feel like a feather!.