Welcome, @Allie_Breeding,
You can do this by adding the rule you showed to your GTM Calendar project. And make a slight tweak–remove the “Add to additional project” part. Also, multi-home the “GTM Launch Date” task in the template in the GTM Calendar project–that will run the rule whereas it will not run rules in the created project for tasks added from the template. See ⚡ Pre-multi-home tasks in project templates, specifically the second section there, which shows this process.
I’m not sure about your Project name variable. If that’s a shared custom field with the project name value, then if you add it to GTM Calendar, I think it would work (but I didn’t test this).
Thanks,
Larry