Don’t try and use the wall as a back support. Use gravity and just tie this into the wall with a brace. See the attached. The red lines show the structure that will support the cabinets. Frame out the cabinets. Also, why did we choose white cabinets? The rest of the showroom is ash furniture. These are really ugly. I would remove the whole kitchen, and do it correctly, and do a darker countertop, wood cabinets, and a fridge with a silver metal door. This is in the center of the showroom where I didn’t want it (it really should have gone in the storage room where it’s out of sight), and now that it’s in the center, the process of no-decision is leading the way, like the wall color. White and cheap. Let’s correct this now and be aware of this dynamic when we don’t discuss and plan correctly. Not your fault as you weren’t involved in the showroom buildout, but a lesson to be learned.