I am not able to replicate this based on the information above. Example:
I added a new QA SelfService Template named Eric Ritter. All the template does is set the Service field value as shown here:
I am able to publish this out to "ALL" if need be and save.
At this point if I login to the application as Self Service User role and go to Service Catalog, select the "Report and Issue" button, I do see my new Template listed as shown below. Am I missing a step on how you are configuring things? By the way this is 2017.3.1.