How do I get the print widget to print exactly the extent the user sees in the web app before they use Print Widget?
I don't want my users to have to experiment with zoom levels and centering points on the map based on what is produced in the print widget output and then going back and forth fine tuning it. I use custom print templates created from ArcGIS Pro layouts with a map above a legend. Could my problems stem from the vertical/horizontal ratio of the online map versus my template ratio? What else might be contributing to this problem?
If I could only count the number of complaints we've gotten from the public on this issue...
Your intuition is correct, the map vs page size ratio difference is the problem. If I recall, there is an option to choose whether the print preserves the scale or extent, which can help. It defaults to scale, but it's hard to tell where the image is going to be "cut" when you print.
There are some custom widgets (Print Plus is a good one) out there that will insert a "frame" that users can use to visualize those cut lines, but they can be a bit clunky.