One more post on this. Hopefully I'm getting close to something reasonable, at least for the moment, and can move on to other things.
I recently had this split mode:
Someone elsewhere suggested horizontal bars, so I tried that too. Animated:
Someone also said the numbers were hard to read, so I tried bigger numbers. Currently there is no number if a unit is at full (10) health. Animated:
Any strong opinions one way or another? If not, I'll probably stick with the last two options and allow players to cycle (numbers -> bars -> no overlay) for now.