The thing with cutting a door underneath is the J1 is actualy just past the front left foot of the unit so you need to cut flush to the edge of the front foot not a bad idea though.
To me it's not the head of the screws being stripped it's the thread but if you can find a screws that have a rough thread it's better and if you look at the bottom piece you dont have much room for a bigger screws.To do it properly you need to drill a slightly smaller hole than the screws you are using then you need to TAP it and you need to counter sink the face plate or you can use a self tapping screws or you can use a wood screw/sheet metal screw without drilling and tapping that should work but finding a small screws that will fit in that spot is not that easy.
I have just opened mine up again, and as you say, J1 is close to the foot. However, on mine it is not quite as close as you describe (I measured it with the base inserted upside-down) , so perhaps there are some slight variations between batches? I have about 2-3mm to spare between J1 and the foot. If the hinged panel opened from the front - backwards, with a single retaining screw at the front-centre, it may just work. When I have tome time, I will try it :-)