I am aware that in the Data API region I can locate the objects and set their object pass index but it is a fairly tedious exercise. Is there an easier way?
You can find it in the Properties Editor, in the Object tab:
You might also find it useful to use a very simple Python script to set different object indices for multiple objects(all selected in this case) at once:
import bpy some_starting_number = 15 for i,o in enumerate(bpy.context.selected_objects): o.pass_index = i + some_starting_number
(You would copy this into a new text block in the Text Editor and hit Run Script with some objects selected)