After some asking and poking around, I finally figured out how to specify a range using the YouVersion Bible app's URL scheme.
Open a range of verses
The Bible book names are specified using their standard OSIS abbreviations.
The only tricky part here was that I was expecting the arguments to be the start and end verses. But, it's actually an enumeration of the verses you want.
And for reference, here are the other available endpoints.
Open to a specific verse
Open reading plans
Take note that this URL scheme is undocumented, meaning it may change with a future update of the app.