Hello
I am also facing exact same problem with Windows 10 update KB4566782 , KB4571756
waited for September patch Tuesday but no luck stuck in update loop second time.
I have tried all things all possible solutions to fix that problem like you mentioned sfc, dism, troubleshooter manually installing update but nothing works for me windows update always showed Error:
0x800f081f
Method 1
I haven't tried Resetting my pc You can if you want to give it a try
Method 2 (That resolved my issue)
Then download the Media Creation Tool from Microsoft website and selected Upgrade this pc
to latest version from the list and keep all files settings apps
It reinstalled windows 10 and replaces all files But this process taken 4 hours for me
to complete depends on your PC specs and Internet connection
After reinstalling windows my sound driver stopped working then I checked windows update
it installed latest sound drivers from my manufacturer and resolved that issue no problems in
sound now
It also installed September patch Tuesday without any errors
I am frustrated during the reinstallation process but all went smoothly for me uploaded the
screenshot after installing patch
I thought Windows 10 update files get corrupted not all but some of them from time So it is showing error
Installing from ISO or repairing files won't worked for me
You have to reinstall windows 10 with Media Creation tool
Or you can wait for Microsoft to resolve this issue with October patch
Hope it helps
Windows 10 version 2004
OS version 19041.508 (after installing update)