There is a FAQ, which explains exactly this:
Note that that archive contains MSI packages with full version in the file name (like “LibreOffice_6.1.3.2_Win_x64.msi”); this is unlike the filenames of the packages offered from LibreOffice download page, where they don’t include the RC version part (“LibreOffice_6.1.3_Win_x64.msi”). You may need to rename the downloaded MSI to exclude the last digit to match the filename requested.
But in general, after you tried to resolve the problem manually (“I deleted everything in the reg edit and everything I could find file wise”), it’s likely that you will need the “Use troubleshooter tool from Microsoft” section of the FAQ. It is a nice tool that cleans up all kinds of corruption in the Windows Installer database state.
No, it’s not “a program integrates itself”: it’s Windows Installer system service, doing its installation job by writing very cryptic registry values, storing backup MSI packages, and so on - and then, when a newer version of the program asks it to check if an older version is installed, the Windows Installer consults all that… LibreOffice itself has no need in all that stuff, it may work just fine by simple copy of its installation directory. But people need the nice features that proper installation brings: system-wide font installation; avoiding multiple versions in parallel; having shell extensions for file icons, properties, and search; keeping the once-chosen install set, and so on.
