Unfortunately, both methods have not worked.
I tried using the SFC tool--it did fix some corrupt files--but no luck getting the updates to install.
Then I tried doing the repair upgrade, but both attempts resulted in a message saying Windows 11 failed to install or something to that order (I forget the exact wording).
At this point, I'm assuming it's an issue with the update itself--so maybe a future patch produced by Microsoft will work better?