What you did was install 4.2, not use TeXLive Utility to try and repair the TeXLive installation of 4.1.

However, it does seem that you now have a complete installation of 4.2 which should work. Open the example document in /Users/Shared/Gregorio/examples and try and compile it. Depending on permissions, you may need to copy the examples folder to your Desktop in order to conduct this test.

You've also got one loose file from the TeXLive installation. Since the TeXLive Utility won't let you remove that, do the following at the command line:

rm /usr/local/texlive/2016/texmf-dist/tex/lualatex/gregoriotex/gregoriosyms.sty

You may need root privileges to do this (sudo). You shouldn't really need to do this, so this is only a suggestion.

Maybe a lead: TexWorks seems to use “2016” files:

This is not a lead. TeXworks doesn't determine which TeX files are used, that's built into the document compiler (LuaTeX itself) and follows a specific precedence order when searching for included files:

1) the current working directory
2) user specific (~/Library/texmf on a Mac)
3) system wide (/usr/local/texlive/texmf-local on a Mac)
4) distribution specific (/usr/local/texlive/2016/texmf-dist for TeXLive 2016 on a Mac when installed using MacTeX)

When you use a command like `\usepackage{gregoriotex}` LuaTeX will look in turn at each of these locations to try and find the file requested. Once it finds it, it stops looking and uses it. This is why our installers (which target the system wide directory) can peacefully co-exist with the package included in TeXLive 2016 (which is in the lower priority distribution specific location).

When you install TeXLive (via MacTeX or any other method) only the distribution specific directories are populated because they are under the direct control of the distribution. The other locations persist across distributions and thus one can change your distribution (as when installing the 1/year upgrade) without needing to reinstall packages which are managed on the user or system level.

Finally, looking at the screen cap of your document, I note in the log that you're still running into an error because of an `&` in your header. `&` is an active character in TeX and must be preceded by a backslash (`\&`) in order to print normally.
--
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Br. Samuel, OSB
St. Anselm’s Abbey
Washington, DC
(R. Padraic Springuel)

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