Removing the undercoating is a noisy affair. The large metal panels vibrate with the tools. So while I hoped the noise wouldn't carry far, I did have a complaint from one of my neighbors who was walking past; it was friendly in nature--the neighbors have been supportive of my efforts. And I want them to remain that way. Fortunately, I was nearly done--so I quickly finished the piece (it only took two minutes.)
I had two pieces left, the trunk lid and the hood. The trunk was a piece of cake--it had a tar-based coating so it was easy to scrape off using a heat gun.
But the hood worried me. For some reason, it had been coated underneath with the same PVC-based undercoating that was used on the rest of the car. And that had required the down-sized equivalent of a jack hammer to get rid of it. What was I going to do?
Fortunately, all the fluids leaking out of the car, and the constant heat cycles, had broken down the undercoating. In certain areas, like the area over the battery, it peeled off in big flakes. And in other areas, although it was fairly solid, it was much softer than what I'd dealt with before; by keeping a flexible putty knife sharp with a small file, I was able to get it off relatively fast--and quiet.
Now it is just a matter of waiting for a place to open up for me at the blaster.