Conjectural uncapped automorphisms in the E8 building over F2

Fix the ordering $\alpha_1,\ldots,\alpha_{120}$ of the positive roots of $\mathsf{E}_8$ according to increasing height, using the natural lexicographic order for roots of the same height. Let $x_i(1)$ denote the corresponding root-group elements in the Chevalley group $\mathsf{E}_8(2)$. An automorphism is uncapped if it maps no chamber to an opposite chamber; its decorated opposition diagram records the types and opposition behavior of its images.

E8(2) uncapped-automorphism conjecture. Let

$$\theta_1=x_{88}(1)x_{90}(1),\qquad \theta_2=x_{88}(1)x_{89}(1)x_{90}(1)$$

in $\mathsf{E}_8(2)$. Then $\theta_1$ and $\theta_2$ are uncapped, with the respective decorated opposition diagrams displayed in the source.

These are conjectural computational examples for the two diagrams of $\mathsf{E}_8(2)$ that the authors could not handle with their computational techniques. They randomly selected $10^5$ chambers and verified the claimed structure on that subset, but a complete verification remains open.