You're on the right page. Do report back on the experiment, but if you can tolerate it - be persistent and give it time. Many have reported success with this method.
If you are concerned about the chemicals involved, might want to research other surfactants. Iodine, apolactoferrin (Biotine mouthwash contains it), yucca root (to name a few) are also known to penetrate biofilm. More tips and clues below: