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Durock is an excellent choice. You can glue it down with panel adhesive. Asbestos would only be a problem if you disturbed it but once the Durock and tile are down then grouted in there would be no way for the fibers to become airborne.

Hi Frank. There's a product out there called Citra solve it works well for removing adhesives unlike other glue removers the fumes are not flammable. Just use as directed on the container. Good luck