Thanks for your guidance, so that't how I should dump the entire flash.
I'm gonna try it and see if it works.
Updating the software from 4.12.1.262 to the latest version 4.12.1.330 did not go so well...
The USBDM Memory Dump tool works fine (as before), but when I run the HCS08 Programmer tool now, I get an error... (see attached screenshot).

Maybe my mistake was that I installed the new version alongside the old version (without uninstalling the old version first)?
I now uninstalled both versions, uninstalled the drivers, rebooted, installed the drivers, install the new version again, rebooted. But I still can't run the programmer, I still get this error
Anybody knows how to fix this? I hope so.