I have the 3200BHT with the rear kitchen and fridge.... thought about reversing the door as well, but figured out what it's that way. If you do reverse it, you can't get the trays/shelves out... unless you bolt it back down in a different spot.
Anyway, just sharing my findings, but i believe i got to the screws under it by taking out the drawer that is under mine.
2010 Tundra DC SR5 TRD 5.7L towpkg (gone)
2008 F350 Lariat CC DRW 6.4PSD
2013 PT Tracer 3200BHT
BlueOX SwayPro (used when hauling cart too)