I'm in the same boat as you, and oh my, there is a real difficulty spike going from the minor axis checking method to the box checking method.

However, I think you should push on with doing it freehand. If you find that the minor axis being wrong is throwing you off, try focusing on the box you have constructed as a reference instead. Part of the reason you draw the box is to check if your minor axis is aligning to the correct vanishing point as well. If you just use a ruler to construct it, you basically throw that out of the things you could learn.

That being said, if your corner lines are off, I don't know if it is a good idea to continue to construct the minor axis line off of something you know is already wrong, or try to guess the correct position based on the box as a whole instead of the two points. Personally I do the latter, because I think that allows me to learn to gauge my minor axis off more than just two points, but I could be wrong about that.