Okay, so I tried it again.
This attempt made a correct default GDB, but still had a connection to the original (See Below, Original = "Template Work"). I tried deleting the original before creating a new project, and while the new project does not recreate the old gdb, it still has the reference, which is super annoying.
I'm also having the issue where the template is acting like a normal project package and recreating all the data, even though it is maintaining and using the original references to the data's location on a network drive.
I do not want this.
Is there a way to create a template that doesn't duplicate data?
It looks like it's doing this because the originals are stored in file GDBs, rather than on an enterprise GDB. Is there a way to get around this without moving the data or switching the layers' sources before creating the template?