Everybody has their own way of removing undercoating: I will add mine that we did for a 67 GTX with factory undercoating.
The undercoating is thick in many places and hard to soften. But if the car interior is out and you can get to the floorboards from inside, try using a propane torch (we used a propane weed burner - example picture below) on the INSIDE of the car on the floorboards. Then (best if you have two people) the second person uses a scraper to scrape chunks off the underside of the car where you heated it. The propane torch will have loosened the bond to the metal, and you'll be able to take big slabs of undercoating off. This technique works really well to get 90% of the undercoating off, and it is a bit less messy than needle scalers, etc.
Good luck whatever method you choose!
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