The point as others have mentioned is to do small tests on INCONSPICUOUS areas of the sideart (not the middle), and find out what works best for that paint, before trying to do large areas on the actual art. Silkscreened art tends to be pretty tough, but depending on what chemicals you use, and more importantly what technique you use (i.e., how long you leave it on, and how/what you use to mechanically remove), you'll need to experiment to get the right combination down that will still look ok after, and not eat into the art. Magic Erasers are good because they're forgiving, and easier to control, even if they require more elbow grease. Better less harsh than too harsh.
Also, every option will work worse if it's cold. Get a heater and warm your garage and the cabinet up.
Test to find what works best on a small white-only spot where it won't matter if you strip too hard, and you'll have an easier time on the rest of the cab.
It's always best to preserve what you can (including t-molding, as repro is never exactly the same as original). Yes, you can strip and wrap the cab with new printed stickers and molding. But it won't be the same as original.