That being the case is separate rescue media the only way, or is there a way to leverage this built in rescue mode with speech?
A separate, "live" distribution offers a lot more tools for working on a system than you'll have in any "rescue" mode of an unbootable machine.
If you can get to a shell prompt and your root file system is
mounted, then of course you can run your screen reader of choice.
In my experience, though, booting from a live image on a USB drive
is generally easier. It's good practice to have one available. If
you're running Debian testing or unstable, you're taking risks, so
having a live distribution that you can boot from is just good
policy anyway.