In the end I had success using a grinding wheel and a 100mm / 4" grinder to remove all the slightly loose chrome. The good chrome under the grips simply wouldn't move, so ended up being ground off by the grinder wheel.
This left a terrible surface, with many small flattened patches and diagonal scoring. It was no longer round. I spent a half-hour with 80 grit sandpaper, then 160 grit then 400 grit paper.
It was a slow process, and ultimately finished, it was no fun at all.
Then I immediately primed the bare steel to prevent any further rust from developing on the virgin steel surface. On top of that I will put several coats of black spraypaint, and then a couple of clear topcoats.
I didn't get a photo of it before painting, but here's one showing one coat of primer. Looks like its been peeled with a vegetable peeler, then zoom in to see the scratches in the "around" direction.
Final edit - here's the finished bars on the scooter. That's two coats of primer, two top coats, and one clear coat on top.
Check out the zoom on this one:
The Stem Cap is alloy and it had white aluminium oxide "rust" , so the same treatment has left a different look. I left the four offset stem bolts chromed and unpainted, because in my experience painting nuts and bolts is a waste of time.