If I had to do my undercarriage all over again, or restore another Cougar in the future, I would have sent it out and had someone soda or media blasted it. Spent way to many long hours on my back. Does soda blasting work at removing rubber undercoating?
I used silica sand to blast the understructure of my "high school Cat" back in the early 80's during the resto-mod work. The inside of my garage was cacooned with plastic, and the exterior of the car was wrapped with heavy cardboard, plastic, and duct tape. I rented a small industrial air compressor from the local rent-it shop that was basically a Ford 302 small block on a trailer that had (1) bank of cylinders converted to an air compressor. And, blasted away for a weekend. Looking back 26+ years, I would not do this again. Nor, would I recommend this appoach to anyone else. Blasting inside was a huge mess, and being young, dumb, and a little gung ho isn't the best approach either. The 3M dust masked being used probably wasn't protecting my lungs. If I were to blast the underside of another car, it would be done outside with use of a proper fresh air respirator.
In address to the undercoating question: Sandblasting did remove trace and/or film amounts of undercoating. Prior to blasting, the majority of the undercoating was removed by using a putty knife scraper and low heat from a propane torch. And, cardboard to protect the garage floor. This process of removing the undercoating is also quite messy, and will require plenty of fresh air, along with skin protection.