Expected classification of even-dimensional quadratic forms of height two

Let $\phi$ be an anisotropic quadratic form of even dimension over a field of characteristic not equal to $2$, with height $h(\phi)=2$. Let $\deg(\phi)=d$. A Pfister form is denoted by $\pi$, and an excellent form is one similar to $\pi\otimes\sigma'$, where $\pi$ is a $d$-fold Pfister form and $\sigma'$ is the pure part of an $(n-d)$-fold Pfister form.

Expected height-two classification. Exactly one of the following holds:

1. $\phi\simeq\pi\otimes\psi$ for some $(d-1)$-fold Pfister form $\pi$ and $4$-dimensional form $\psi$ of nontrivial discriminant.
2. $\phi\simeq\pi\otimes\psi$ for some $(d-2)$-fold Pfister form $\pi$ and $6$-dimensional form $\psi$ of trivial discriminant.
3. $\phi$ is an excellent form of dimension $2^{n+1}-2^d$ for some $n>d$.

The statement is presented as the expected classification in the characteristic-not- equal-to-$2$ theory, in a discussion explicitly describing the problem as open.