there is a product out that will strip this stuff. I have only heard of it off this board.
I have encountered this before and a non chemical way is completely OUT. This stuff with heat and time actually welds to the wood. Sanding is out, scraping is ridiculos, and only hope is some chemical.
I have just sub floored over this and started new, but I understand your plan.
Go to a Paint Dealer and describe your situation and ask for help.