I have all of my source file from my old WP site that I have from backups and a CPanel dump where I was using the Avada theme. I have all the theme files and whatnot, but is there a way I can extract or re-zip the theme from these files so that I can properly upload it on the new version of my site?
The easiest way to do this is to upload them using FTP. You can use a free program like Filezilla to upload your files to your server.
You will need to know the host name (usually just your domain), user and password. If you don't know this info your hosting company will be able to assist you.
Once connected, find the folder where WP is installed. This is typically inside of
/public_html/. Your theme files are located in
/wp-content/themes/avada/. You can upload your backup there.
I would make sure you have current backups before doing anything.