This might be quite an undertaking and if you are only doing it because of your concern for asbestos, you should consider that drilling screws thru existing surface to mount new drywall will disturb and make airborne more of it than if you just painted over it. First thing I'd do is check to see if in fact you have asbestos. You can contact your state enviromental agency for information on getting your walls tested. Luck, Kizmet