How can I get that translucent effect on Jack O' Lanterns?
Obviously you need to remove more material in order to allow light to shine though. You know that much. 


  However, whenever I try I either can't get the husk thin enough, or I go too thin and bust through.


What you need are depth checkers spaced around the surface of the lantern where you are trying to achieve this effect. 

Toothpicks would be an easy suggestion for this. Put the pick in and feel the the inside of the pumpkin for where it is going to come through. You don't want the toothpick protruding the inside. That would negate its purpose as a depth check. You know it is inside enough once you barely feel it with your fingers. Putting it too far through might make it move easier which would again reduce its effectiveness. With enough toothpicks you can then use the portion that is outside of the pumpkin to gauge the thickness near the toothpick. 

While I cannot find a picture of this being done to a pumpkin (yet!) a similar principal is used when making a quinzee. They use sticks to make sure the whole structure is of the same thickness. 

 

Likely, the tactic I described above, is what was used in your first picture.   Look at where you see the pinholes of light coming though. I have used MSPaint with awesome circles to draw attention to the holes.