Hi Thomas,
I would probably suggest that you use a separate field for the Group you want to assign your Incident to. Since you are using a template you can fill this field in within your template as well. This is then a field you can hide on the window so that your end users doesn't have to see it.
There should already be a Group drop down list on your Incident Object called: "Suggested Group". Add this to the window if this is not already on there and fill this in in your template.
To then get the Incident to assign to this group you add in an automatic action in the process where you right click and select a value type in the Group field and select the Incident.Suggested Group attribute.
Kind Regards,
Jenny