Installation - Root Document Change

I'm (still) having some trouble installing Grav. I may have a similar problem as this person had:

https://muut.com/i/getgrav/installation-configuratio:problem-with-shared-hosting

I'm running php 5.6 as verified by a php info test. My main domain, on which I intend to install grav, is pointing to the public_html root folder by default. My hosting provider would not let me change the document root to public_html/grav. Inside public_html I have sub folders for other addon domains which work fine.
If I leave the unzipped grav installation folder untouched inside public_html I get the following:
error log: cannot serve directory /home/XXXXX/public_html/: No matching Directory found, and server-generated directory index forbidden by Options directive
output: Forbidden - You don't have permission to access / on this server.

which makes sense if the document root is pointing to public_html rather than public_html/grav

However, If I move all the grav folder contents up to public_html directly I get this:
error log: SoftException in Application.cpp:261: File "/home/XXXXX/publ ic_html/grav/index.php" is writeable by group
output: Internal Server Error - The server encountered an internal error or misconfiguration and was unable to complete your request.

Since I cannot change the root folder directory so that my main doamin rests "inside its own distinct folder" is there a workaround for installing grav? Or do I need to find another hosting provider?

You probably just need to move all the filies and folders to your web root. It's pretty easy to do from the shell, and probably also from cpanel filemanager. Just make sure you move all the files and folders including the hidden ones that start with a .

thanks, I enabled all dotfiles in cpanel and moved all data to public_html. Same result: Internal error 500.
Do I need to run composer to work on the other proposed fixes from troubleshoot:
1) updating php.ini
2) options - indexes
Can I use composer with a shared hosting account at all?

You don't need to run composer if you downloaded/installed one of the pre-build packages as linked to from getgrav.org. You would need to run composer if you installed via git or downloaded the zip package directly from Github (as this wouldn't include the vendor packages).