I have never used this particular product, but the concept is sound. It appears to be a non-volatile emulsion type organic solvent that should work to dissolve the mastic. I have used citus solvents that are related but produce a strong odor. Hope you will report back if it is successful.
As you know, the asbestos content in mastic is an artifact you don't need to be concerned about unless you intend to sand or grind. Your proposed methods are safe.