I agree that by design Flatpak aims to provide a secure environment through sandboxing; in practice, the implementation has gaps that can lead to security risks, particularly when apps are granted extensive filesystem access. This can undermine the effectiveness of the sandbox and potentially expose systems to vulnerabilities. HOWEVER, being on an immutable system, these risks are mitigated to some degree.
I'm particularly hopeful for Flatpak's promise of fine grained permissions. Flatpak is developing a fine-grained permission system with portals for external interactions, BUT this system relies on integration with toolkits like GTK, rather than app-specific APIs, complicating its implementation. There is more info in the linked article in the previous post, and here it is again.
Admittedly I'm not familiar with distrobox, but my caution is for any approach that distributes containerized programs with their own runtimes; they proved to be a real headache on my "mutable" system and my nvidia GPU until I switched to rolling OS.
I'm glad you found some candidates to potentially resolve your issue. What distro did you end up using? I'm curious to give it a go next chance I have some free time. Cheers.