For some reason I'm having issues overriding files. If I didn't have OS ticket installed already, could I just upload the contents of the awesome OS ticket archive and start fresh like that? Is there a way to install the theme without installing OS ticket first?

Actually, check this out:

Can I upload osticket, install it, , backup the congif file, then delete all the files, then upload the contents of the awesomeost archive to the server and then replace the config file?

There is something wrong on my end. I tried installing everything according to your instrcutions and they worked fine but had some bugs. Then, a few days later, i tried reinstalling and I havent been able to get the files to overwrite properly since. So now I am unable to overwrite any files.

You don't seem to understand that the ost-config.php file points to the database.

You were using your old ost-config.php file pointing to the database that no longer exists.
 
osTicket Awesome now works in the support subdomain, and you also have osTicket working in the support-old subdomain.

Before you ask, you'll have to recreate your color theme settings, etc. because you deleted your old database.

Good luck.

Do you have access to my server?