While I assume that you edited your post because you found the answer yourself, I figured just in case I should go ahead and answer the question anyway.

The only issue here is that I think you have the order of operations reversed, at least in your phrasing. What we're estimating is the ellipse itself. We define three out of four edges of the given plane, and then try to place an ellipse in there that fits the given criteria. We define the last edge of the plane last.

It is an estimation, as you said, but that's something we worked on in the cylinder challenge when going through the cylinders-in-boxes. It won't be perfect, but you've already demonstrated the capacity to estimate those proportions reasonably well.

Of course, using an ellipse guide can also help here, though since you're stuck to specific degrees, you may need to work around that when constructing your original 'unit cube'. To that point, if you just start with a given ellipse, use its minor axis to define one vanishing point and then use the requirements for the contact points for the other, you can sidestep not having the 'perfect' ellipse for a set situation.