Problem getting bad disk out of superdrive on a Mac Pro 2010/2012?

I cleaned both optical drives in the Mac Pro, put them back in the case, then found that the disks themselves were dirty enough to make them (temporarily) useless as install disks. But the condition of the computer made it impossible to get the disks out of the drives by the usual means. This is a Pro, with the cheesegrater front and back. I used a flashlight and a paper clip to try to find the emergency eject hole-no joy there. I read in another string that the user can pull down the front metal door over the drive to find out where the hole is, and that was successful. However, even if you can use that knowledge to locate the hole-after closing the metal gate- by dead reckoning, that does you no good because the metal door has to be closed(i.e., out of the way) in order to reach the hole, meaning that the plastic tray may attempt to move forward...until it encounters the closed metal door.Then it can't move forward any further. So you can either not find the hole and be unable to open the drive, or find the hole and be unable to get the drive tray past the case's metal door.

The only way I found to get around the problem was to shut down, unplug, open the case, pull the optical drive shell out halfway, poke the hole with a paper clip, take the disc out, and, after checking the drive connector cables, slide the drive shell back in and close the case.