Just to add on the method I was taught...the reason you do a circle is so that the dog never picks up on the fact that its just a straight line and there will be something good at the end of it for them. The circle never really ends, and so the dog can keep going and going and there isn't a super high value item in there. The point isn't to advance your dog as fast as possible (although I know you really want to), but to really instill good tracking habits in them early. The way I learned we also don't hold the long line at all, just let it drag behind the dog. This way, you guarantee that as a handler you aren't helping at all. Every time you corrected her, to get her back on the track, would be either points or a non qualification. You really don't want the dog to depend on you at all...because in a trial you won't know where the track is, so if she loses it, and you just make her go back to where you think it is, you might be completely off.
It is pretty good that she can take turns, and also cross paths where other dogs/people have walked, but her finish isn't tracking at all. She knows the thing is there and she's going to go get it.