How do I overwrite a corrupt Windows 10 installation while preserving files?

Background: I accidentally force-shut my Windows 10 PC while it was in the process of shutting down yesterday by holding the power button. When I try to turn it on now, it either 1) complains about Secure Boot, or 2) when Secure Boot is disabled, goes to a BSOD with the error code 0xc0000428.

The Problem: I would like to overwrite the corrupt Windows installation with a fresh one, while preserving files and folders. So I went to https://www.microsoft.com/en-us/software-download/windows10/ on another Windows 10 PC, downloaded the media creation tool, and saved installation media to a USB stick. Then, I booted from the USB stick in the PC with the corrupted installation.

However, after selecting language/region/keyboard and accepting the license terms, I ran into an issue. At that point, you are offered a choice between Upgrade: Install Windows and keep files, settings, and applications which upgrades Windows & preserves your files, and Custom: Install Windows only (advanced) which does a clean install and deletes your files. I wanted to keep my files, so I chose the first choice.

Unfortunately, when I do so, I get the following message:

The computer started using the Windows installation media. Remove the installation media and restart your computer so that Windows starts normally. Then, insert the installation media and restart the upgrade.

But since I can't boot into the corrupt Windows installation, I can't follow these instructions.

My questions are,

1. Is it possible to get the installer to do a fresh install of Windows 10, preserving existing files, without having to boot into the corrupt installation?

2. If not, what are my other options for performing the reinstallation while preserving my data? I have an all-in-one, so I'm not sure if it's possible to extract data from the inner hard disk so I can perform a clean install and restore them later.