Did some more digging, here's what I've observed.  I'm starting to think there are two separate issues:

Missing Champion HUD images:

Strategic map: Armies led by champions generate a green-hued picture in the army HUD, instead of an image of the army's leader.  Only the image is broken, the object iteself is still clickable.

Tactical map: In the turn-order column in combat, champions also generate a green-hued box.  Also, their "card image" in the lower left-hand corner does not appear (it's just blank).  Sovereign and summoned unit (Sand Golem) do appear correctly in the initiative HUD. 

Missing Trained/Trainable Unit images:

Strategic map: Armies led by trained units generate a green-hued picture in army HUD.

Strategic map: The unit training window has empty, gray colored squares where unit images should be.  However, the unit image does appear in the queue when it's ordered to be built.

Yes, I uninstalled and deleted the beta files.

Yes, I am running as Administrator.