Anagnostopoulou-Merkouri and Burness's unrestricted regularity conjecture

Let $G$ be a finite almost simple group with socle $G_0$, and let a non-standard subgroup mean a subgroup whose associated primitive action is non-standard in the sense defined in the source. Anagnostopoulou-Merkouri and Burness's conjecture. Every $7$-tuple of non-standard subgroups of $G$ is regular.

This conjecture asks whether the conjugacy condition in Cameron's solved formulation can be removed, and is presented as a conjecture from Anagnostopoulou-Merkouri and Burness (2024).