One could just have the contacts wired differently on the otherside of the board. The larger problem would be the contacts in the "backside" of the plug getting

One could just have the contacts wired differently on the otherside of the board. The larger problem would be the contacts in the "backside" of the plug getting shorted by the USB connector shield. Outside of that it does sound doable. Maybe with a thin pcb and a USB-A shell it'd be doable...