We are selling our home and would like to install a backsplash behind our new kitchen island stove and along the back cabinets of our kitchen island "wall". To be more clear, our island is two tiered. The lower tier is where the stove is installed and the upper tier, which is made of cabinets topped with quartz is where the stove backs up against.

The issue I'm looking to solve is that the back of the cabinet that the stove sits against is a flimsy fiberboard of some kind. There are 3 cabinets and where the cabinets abut there are 1/2 particle board. Meaning that I need to install a suitable backer board attached to the fiberboard and there is only a 1/2 inch particle board to screw in to at the ends of the counter and where the cabinets abut. I'm concerned about screwing in as having such a small area to screw in to coupled with the possibility of a screw coming out the side and damaging the cabinet would be a disaster.

What I would like to do is glue the backer board to the fiberboard if at all possible. I am not sure what I can or should use to glue it or if I should even do that. I do know that the walls of the cabinets are most likely glued on but I dont know what glue the manufacturer uses.

I have done several tile installations before but none where I didn't screw down the backer board.