I'd like to express my complete surprise that printing multiple map layouts in a project isn't part of the product that's shipped with this software since day 1!
If ArcGIS Pro is to be promoted as being able to create multiple layouts in a project as a selling point compared to ArcMap, you should also likewise have the ability to print all layouts, or a subset of layouts selected in a dialog box.
Automating a print from a Map Series is nice, but not viable for my particular use in this case. Rummaging through the scripting tutorials right now.