I created an app on AGOL using the story template. I used the National Geographic template.
The zoom interval is too large so that when I zoom in only once, most of my state is outside the extent, but if I zoom out once then the state is too small.
Hosting the app on my own server is not an option so I can't use any of the script fixes.
As Kyle mentioned, you can't do fractional zoom levels. This has been a thorn in my side, too - I called and spoke with Esri - they said there aren't any plans to change it in the foreseeable future. If this is ever an option for you down-the-road, you may want to consider Levels of Detail (LODs):
If you develop you own app in web app builder developer edition its possible, but with AGOL templates unfortunately no. I am in the same position as OP. My municipality does not fit well with the current zoom scales...