Shoot....this really is terrible. Are your cabinets ruined or warped? That's what I'd be most concerned about. The fabric is an easy fix. Wood that's been soggy for a while, that's a different scenario:<
We had a leak in our roof last year that came through my sewing room closet into our livingroom. It didn't do any major damage, but it really was stressful. So sorry you're having to deal with this.