I like Seth's solution, but then again, he's the definitive Systainer dude! <we are not worthy emoji that doesn't yet exist>
I will suggest getting the scraper attachment. Makes pulling veneer off pretty easy. Also used it to correct parts of my floor before applying new flooring (engineered flooring and tile). Don't neglect to notice that you could drill 2 holes in the scraper for shop-built accessories that you simply screw on/bolt-on.