The shop that did my car said they have done cars on a drive-on lift and alot of taping/ masking off etc. They use plastic media as far as I know.
The guy said he spends hours masking and covering everything for protection.
I sandblaster my coupes underside after removing everything. I put it on jackstands and was on my back daily for several weeks using a small siphon blaster. It was a PITA, I got sand everywhere but it did a great job removing paint, rust, undercoating and crud. I then sprayed epoxy primer for protection.
If I had it to do over, I'd strip the car and take to a professional, that way it would all be done at the same time, including the body. That would be money well spent, at least for me.