In Advanced settings > Advanced backups there is an additional setting to ignore bad sectors. I needed to check that as well.

@Silbee changing Macrium Reflect settings to skip verification of the file system and ignore bad clusters enabled me to create a backup indeed, so if you add that as an answer I'll accept it.

@JoepvanSteen I've added the SMART screenshot. I guess it gets relatively hot even though I'm not doing much right now. I assume it gets even hotter at times when CPU and/or GPU are heavily used.

@Silbee elaborate chkdsk I had tried already. I can skip MFT check, but then during backup I get the CRC error that I got the first time again.

This worked so I'll accept the answer, thanks! Meanwhile I found out that booting into Safe Mode should have worked as well: superuser.com/a/1452916/101809

I'm writing this on a system with a new Samsung 970 EVO Plus NVMe onto which I restored an image that came from an SSD in MBR format, and it works without converting. Just had to make sure the NVMe driver was enabled before creating the image.