Thanks for your answers, all! I have a solution!
Richard, I did notice and quickly read through your Orient Express topic, before I posted. I thought it was a pretty cool coincidence how similar it was to my query! Though, what I wanted & what the solution is, are simpler and didn’t involve the Vertex Modeler or hotpoint adjustments. Basically, I wanted to quickly & accurately rotate an object (axes & all) to align (face the same way) as another object, ideally without moving either from their positions. Your, and Sockratease’s mentioning of grouping objects to give them a common XYZ, and DougS’ mentioning of changing the properties panel figures, gave me an idea to the solution of matching the rotation/orientation of object A to object B:
1. parent object A to object B
2. zero out all A’s rotation numbers in the properties panel. A will face the same way as B, without either leaving its position
3. unparent A from B and A’s rotation numbers will automatically be right for world coordinates
Well, that solution worked for 2 simple cones, anyway. Hope it’ll work for complex figures & tree structures, also!