@mitcorb said:
I think the tool is aligning with the nearest segment of the circle that forms the cylinder, since you mentioned that 7.5 degree offset. Again, this is just a guess.
This is correct.
Unfortunately, for symetrical shapes like circles, this may not represent the intuitive orientation. I am afraid there is no magic fix in the general case.
The best is simply to orient the box manually to the desired direction (click on an edge in the model, or using the arrows for aligning on model axes).
Fredo