Wall between garage and living room has fire rated drywall on one side and cabinets on studs (no drywall) on other. Need advice – GreenBuildingAdvisor

We discovered an unfortunate situation: the house we bought has no drywall behind the custom shelves/cabinetry in the living room. On the other side of the wall is the garage.

The garage side does have 5/8 drywall, but I highly doubt it is fire-rated. On the cabinet side, there is only plastic, and the walls are insulated with fiberglass (see picture). It also happens to be the central location for mice nests. I’m going to demo and redo that garage wall this week because the mouse situation will worsen quickly, given it is fall.

My plan is to at least demo the drywall on the garage side, take out all the fiberglass, and fill the wall with Roxul. Then install fire-rated drywall on the garage side.

Where I am unsure is how to address the cabinet site of the wall. Moving cabinets, even temporarily, would be expensive because it is all custom-made.

Air infiltration is what I would like to stop, because last winter, when we got the place, I very quickly discovered how drafty that area was, even with the garage doors closed. On cold days, the furnace was running nonstop.