Have you tried using a heat gun to soften the adhesive underneath the veneer. If it works, you may be able to pull the veneer off in large sections.
I'd try to heat up a corner and get a putty knife underneath. Then insert a dowel rod or a piece of scrap. Keep moving the dowel or scrap in so as to keep "pushing" the veneer pulling up from it's underside. As you heat the veneer, if it softens the adhesive, it will release. Move the dowel, heat, repeat.
Watch your fingers too. Heat guns - even cheap ones - can reach temps over 1,000 F.