Unable to install SSMS 18.x, error 'Could not access network location *:'

I have had SSMS installed in the past, and attempted to upgrade from 18.5 to 18.6, but I received the error above. Since then I am unable to install/upgrade to 18.6 or 18.7, nor am I able to uninstall 18.5.

It seems this might be the errors. Google hasn't been of much use. My guess is either something corrupt in C:\Program Data, or Windows registry.

[3870:3AEC][2020-10-22T16:46:00]e000: BootstrapperEngineDataModel.OnError: Burn engine encountered error. PackageId: SsmsPostInstall_x64, ErrorType: WindowsInstaller, ErrorCode: 1606, Data: 1606,*:, ErrorMessage: Could not access network location *:., UIHint: 5
[3870:3AEC][2020-10-22T16:46:00]i000: MainViewModel.AddFailedCondition: Error: SSMS Post Install Tasks: Could not access network location *:.
[3870:3AEC][2020-10-22T16:46:00]e000: MainViewModel.OnPackageError: setup failed for packageId: SsmsPostInstall_x64, package: SSMS Post Install Tasks, errorCode: 1606, errorMessage: Could not access network location *:.
[3870:3AEC][2020-10-22T16:46:00]e000: BootstrapperEngineDataModel.OnError: Burn engine encountered error. PackageId: SsmsPostInstall_x64, ErrorType: WindowsInstaller, ErrorCode: 1606, Data: 1606,*:, ErrorMessage: Could not access network location *:., UIHint: 0
[3870:3AEC][2020-10-22T16:46:00]i000: MainViewModel.AddFailedCondition: Error: SSMS Post Install Tasks: Could not access network location *:.
[3870:3AEC][2020-10-22T16:46:00]e000: MainViewModel.OnPackageError: setup failed for packageId: SsmsPostInstall_x64, package: SSMS Post Install Tasks, errorCode: 1606, errorMessage: Could not access network location *:.
[0614:3DCC][2020-10-22T16:46:00]e000: Error 0x80070643: Failed to install MSI package.
[0614:3DCC][2020-10-22T16:46:00]e000: Error 0x80070643: Failed to execute MSI package.
[3870:3AEC][2020-10-22T16:46:00]e000: Error 0x80070643: Failed to configure per-machine MSI package.
[3870:3AEC][2020-10-22T16:46:00]i000: MainViewModel.OnPackageAction: Install Completed for package SSMS Post Install Tasks
[3870:3AEC][2020-10-22T16:46:00]i319: Applied execute package: SsmsPostInstall_x64, result: 0x80070643, restart: None
[3870:3AEC][2020-10-22T16:46:00]e000: Error 0x80070643: Failed to execute MSI package.

The full log file (with truncations around the progress bar) is here.