Perhaps try booting via USB without affecting the internal system at all?
I normally give this advice in the context of using Linux in a way that is certain to not tamper with an existing Windows installation, but for your context it would be equally valid.
The idea is to run your new/replacement Linux directly from a USB drive - i.e you boot it from the USB port.
I've detailed the method here - https://dev.to/geraldew/ubuntu-linux-installation-to-a-usb-external-drive-with-efi-boot-46pj - but a caveat is that I wrote all that as a tech description rather than a friendly "how to" guide.
In your case, having created and then booted such a system, you would then mount the computer's internal drive to access or copy off the contents that you wish to migrate. (Note: drive encryption and Windows fast boot affects the ability to do that - it's not my use-case so I don't cover it.)
BTW when the internal drive was spinning platters and the external is a USB3 SSD then this might even produce a faster system.
Biting the hand that feeds IT
