Error 1639 Reporting Services - Native failed with errors SQL Server 2012

Error 1639 Reporting Services - Native failed with errors SQL Server 2012

I get Error 1639 when attempting to install SQL Server 2012 Reporting
Services. My research, conclusion, and question about a resolution are all
outlined below. Thank you in advance for your help.
Research:
Reason for failure: An error occurred during the setup process of the
feature. Next Step: Use the following information to resolve the error,
and then try the setup process again. Component name: SQL Server Reporting
Services Component error code: 1639
I successfully installed sql svr 2012 reporting services successfully
installed on this machine in May. I tried removing it last week with some
errors, but I thought I was successful. Now, however, I get the
aforementioned error. All other features and services install to the same
box w/o error.
A look at the installation log reveals: * Product: C:\SQLSVR2012 iso
files\x64\setup\sql_rs.msi * Action: * CommandLine: **** MSI (s) (90:50)
[12:25:40:082]: Machine policy value 'TransformsSecure' is 0 MSI (s)
(90:50) [12:25:40:082]: User policy value 'TransformsAtSource' is 0 MMSI
(s) (90:50) [12:25:40:136]: Machine policy value 'DisableUserInstalls' is
0 MSI (s) (90:50) [12:25:40:136]: Specified instance
{DCCB1789-1DA0-4E3A-A52F-7815B602CC98} via transform
:InstID01.mst;:InstName01.mst is already installed. MSINEWINSTANCE
requires a new instance that is not installed.
That log entry led me to check for this Instance in the registry and
compare it to other registry keys, for example the adjacent SQL Server
2012 Database Engine Services key.
Conclusion
It seems all features/services except the Reporting Services were
successfully uninstalled then re-installed as the InstallDate key as been
updated for everything else (all features/services) except for Reporting
Services.
Question
So then, my question simply is how do I safely remove the key for the
Reporting Services installation entry? Is it simply a matter of removing
all references to that key and attempting to add features back to SQL Svr
2012 though the normal re-installation process? There are 3 such
references that I found when searching the registry:
Components -
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Installer\UserData\S-1-5-18\Components\E2D8041188B416A4BA3DC8F76D0F4E0B
Products -
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Installer\UserData\S-1-5-18\Products\9871BCCD0AD1A3E45AF287516B20CC89
Uninstall -
HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Uninstall{DCCB1789-1DA0-4E3A-A52F-7815B602CC98}
Thank you in advance for the help.