How to execute DISM from Windows 10 PE on Win 10 system with Windows Update / Microsoft as source only?

I've got a corrupt Windows 10 installation (SFC noted Windows Resource Protection found corrupt files but was unable to fix someo of them...) so I tried to run DISM, from a Windows 10 PE USB installation. (Note: Win10 PE current OS is at c: and offline system on system is at i:)

Here's what happened: #1:

c:\Windows\system32>dism /image:i:\ /cleanup-image /restorehealth

Deployment Image Servicing and Management tool
Version: 10.0.18362.1

Image Version: 6.3.9600.18384

[==========================100.0%==========================]

Error: 0x800f081f

The source files could not be found.
Use the "Source" option to specify the location of the files that are required to restore the feature. For more information on specifying a source location, see http://go.microsoft.com/fwlink/?LinkId=243077.

The DISM log file can be found at C:\Windows\Logs\DISM\dism.log

So then I wrote Windows 10 2004 iso (via Rufus) to a USB so that I've have an install.esd in place to see how that might work, but it likewise failed: #2:

C:\Windows\system32>dism /image:i:\ /cleanup-image /restorehealth /source:esd:K:\sources\install.esd:1

Deployment Image Servicing and Management tool
Version: 10.0.18362.1

Image Version: 6.3.9600.18384

[==========================100.0%==========================]

Error: 0x800f081f

The source files could not be found.
Use the "Source" option to specify the location of the files that are required to restore the feature. For more information on specifying a source location, see http://go.microsoft.com/fwlink/?LinkId=243077.

The DISM log file can be found at C:\Windows\Logs\DISM\dism.log

How can I guarantee that DISM pulls all appropriate files from Microsoft to repair an image (Windows installation) with the correct version, etc?

UPDATE: On #1 I was hoping that DISM would pull in the appropriate image files via Windows Update, but perhaps it doesn't and thus I tried #2. On #2 it was suggested that you must have a matching .esd or .wim file, so I found an old copy of Windows 10 Version 1903 I had previously floating around and put that onto a flash drive via Rufus. I then attempted to execute DISM again with that, but met with failure likewise, but this time also captured the dism.log output:

C:\Windows\system32>dism /image:i:\ /cleanup-image /restorehealth /source:wim:K:\sources\install.wim:1

Deployment Image Servicing and Management tool
Version: 10.0.18362.1

Image Version: 6.3.9600.18384

[==========================100.0%==========================]

Error: 0x800f081f

The source files could not be found.
Use the "Source" option to specify the location of the files that are required to restore the feature. For more information on specifying a source location, see http://go.microsoft.com/fwlink/?LinkId=243077.

The DISM log file can be found at C:\Windows\Logs\DISM\dism.log

The log output can be found here in this gist.

With the 1st error I noted in the dism.log, being the following:

2020-06-19 18:17:35, Error                 CBS    Cannot add wim: file source because it is not supported during offline servicing [HRESULT = 0x800f082e - CBS_E_NOT_ALLOWED_OFFLINE]

I figured I should try mounting the install.wim via:

K:
cd sources
K:\sources>mkdir c:\mount
K:\sources>dism /mount-wim /wimfile:install.wim /index:1 /mountdir:c:\mount

And then I tried to run dism again:

dism /image:i:\ /cleanup-image /restorehealth /source:c:\mount

Deployment Image Servicing and Management tool
Version: 10.0.18362.1

Image Version: 6.3.9600.18384

[==========================100.0%==========================]

Error: 0x800f081f

The source files could not be found.
Use the "Source" option to specify the location of the files that are required to restore the feature. For more information on specifying a source location, see http://go.microsoft.com/fwlink/?LinkId=243077.

The DISM log file can be found at C:\Windows\Logs\DISM\dism.log

Notice errors began to appear around line 253 here in the new dism.log, but I'm not sure why since I'm using a mount wim now: dism.log gist