This is the current plan. First, cover the exposed cabinet sides with thin plywood or make false panels. Then I'm going to resaw solid wood to 1/8 inch and recover the rails and stiles. I'll use wide enough strips to cover up any out of plumb stiles, fill in with wood behind the overlay and use a trim router with a top bearing to trim the fill flush with the overlay and square corners with a chisel. Anyone foresee a problem?
My three favorite things are the Oxford comma, irony and missed opportunities
The problem with humanity is: we have paleolithic emotions; medieval institutions; and God-like technology. Edward O. Wilson