Removing undercoating

First off, I didn't have a welder yet, but wanted to get started on the car. I had a lot of extra wood kicking around, so I built a rotisserie out of it. I started off with the wire wheel method, what a pain and a mess. Someone on a Porsche forum talked about using a needle scaler from Northern Tool for 20 or so dollars. What the heck, give it a try, and it was working pretty well, but very noisy, drove the neighbor crazy. When I got to the transmission hump, the undercoating was just falling off. It had been soaked in trans fluid, then sat in the garage until I started the project. The factory paint underneath was perfect, so this got me to thinking. I sprayed it down with PB blaster and let it set overnight, The next morning the undercoating came off like nothing, with putty blades, without scratching the factory paint if you are careful. Some areas needed a second helping.
I then bought the biggest bottle of Dawn I could find, and went at the underside with a few different brushes. I followed that up with a thorough cleaning with the pressure washer.
Before I get around to paint, I'm sure I will be cleaning it a few more times, so I am sorry I don't have long-term results yet for you, but this was one way to get the job done. Nothing feels greasy or oily, so I'm pretty sure everything will be fine.