Microsoft Office 2016 fails to install with errors 1603, FC73469E

I am attempting to install Microsoft Office 2016 Pro Plus (classic, not click-to-run)

The installation fails, here is an excerpt from Windows Event Viewer:

Fault bucket 124669380009, type 5
Event Name: OfficeClassicSetup
Response: Not available
Cab Id: 0
Problem signature:

P1: 16.0.4266.1001
P2: OSETUP.DLL
P3: 16.0.4266.1001
P4: 1603
P5: Unspecified
P6: FC73469E
P7: 1603
P8: 
P9: 
P10: 

Looking through the event log, I found this line:

'CAInstallLicenses:  Error: Failed to install license. HResult: 0x80070005. '

Following it, there are many variations of this error with a bunch of DLLs:

'07/19/2016 12:57:45.679 [2300]: Assembly Install: Failing with hr=80070005 at RemoveDirectoryAndChildren, line 384
'
2016/07/19 12:57:45:679::[2780] MSI(INFO): '07/19/2016 12:57:45.679 [2300]: Detailed info about C:\WINDOWS\assembly\tmp\XKNCYCIC\OFFICE.DLL
'

Error 80070005 appears to be a permissions related issue. I have verified that SYSTEM has full control of C:\Program Files(x86)\Microsoft Office (though not the parent folder) and C:\WINDOWS\assembly.

• I am running as administrator
• I have tried this with a "clean boot" so hopefully there's no antivirus blocking anything
• I am installing Microsoft Office 2016 Pro Plus 32-bit
• I am running Windows 10 Enterprise 64-bit

Can anyone help with this error? I can post the full installation log upon request.