I used the biggest Phillips driver that would fit through the hole. There's no screwing involved, the driver is only used as a lever so you could use anything (round steel stock?) that fits. Just put the lever into the hole and angle it backward - toward the centre of the door - against the hole...
OK - so for completion in case anyone else ends up looking for a similar solution. I was able to get the cover off by placing a phillips screwdriver into the adjustment access hole and prying the driver so that it just flexed the 'clip' part of the cover off the lugs to release the cover. All...