OK fist, I'm not 100% sure the issue is graphics driver related, especially if your not getting a display before the OS even boots (aka. can't get into the UEFI/BIOS, no system posting graphics).
I didn't realize you had encrypted your drive/partition. This could also cause issues if the system doesn't or can't decrypt prior to needing access. However, you wouldn't need access to /home or /DATA to fix system issues, you only need to be able to chroot (change root) the systems. This means mounting and having access to /, /etc, /usr, and so on from the installed system instead of the live environment. Since only the base of the system changes, there is no need to access your personal data.
I didn't realize you had encrypted your drive/partition. This could also cause issues if the system doesn't or can't decrypt prior to needing access. However, you wouldn't need access to /home or /DATA to fix system issues, you only need to be able to chroot (change root) the systems. This means mounting and having access to /, /etc, /usr, and so on from the installed system instead of the live environment. Since only the base of the system changes, there is no need to access your personal data.