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
1youversion://bible?reference=PHP.4.4+PHP.4.5+PHP.4.6+PHP.4.7
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
1youversion://bible?reference=JHN.3.16
# Open bookmarks
1youversion://bookmarks
# Open reading plans
1youversion://reading_plans
Take note that this URL scheme is undocumented, meaning it may change with a future update of the app.