I also spent way too much time trying to find the alternate mine entrance. I was able to rescue Williams and kill the two guards downstairs (I was level 18), but could not handle the 4 upstairs guards. I looked all around and could not find an entrance, but I think it is supposed to be in the goblin camp where Yup'ik was. It seems like the door to the mine office should not even be accessible if the quest cannot be advanced until after the Battle Tower.
