Question about Moving Electrical Box for Range Hood

I installed a receptacle for my wall mounted range hood. Unfortunately, I placed it too low, and it needs to be raised. The hood requires a minimum height of 30” above the range, and I can’t meet that. I have a glass subway tile backsplash, so it will be a pain to do this. I guess my option is to cut a new hole with an angle grinder or to use some type of surface mounted box. I’ve only ever installed a surface mounted box outside (weatherproof box), so I don’t know if there is something NEC approved for inside use. My thinking is that I would drill a 1/2” hole through the backsplash and drywall and then feed the cable into the back of the box. The chimney runs to the ceiling, so it will hide the box. I appreciate any suggestions/advice. I’m so mad at myself for not getting the height correct the first time.