Causes of thin-shelled chicken eggs

After splitting up our duo of two-year old Golden Comets, it quickly became clear that our guess was right --- one was laying daily and the other was either not laying at all or was laying shell-less eggs that she crushed and consumed.  I'm guessing in favor of the thin-shelled eggs based on having seen one or two eggs with papery shells in that tractor over the last few months.

Calcium is the obvious solution to eggshell problems, so we dosed the troubled hen up with leftover eggshells.  She nibbled on some, ignored a lot, and still didn't lay.  With the simple solution out of the way, I started researching what might cause a hen to lay thin-shelled eggs.  Here are some possibilities:

• Defective shell gland.  The only option is to cull the bird from the flock.
  
• Lack of vitamin D₃.  This would be the best case scenario, but is by far the least likely since chickens become deficient in vitamin D when they are not exposed to greenery and sunlight.  Our birds spend their whole lives on grass in the sun.
  
• Egg drop syndrome.  This viral disease is unlikely to have made its way into our flock, but there is a very slight possibility that our troubled hen could have picked it up by drinking creek water contaminated with duck feces.  Birds infected with egg drop syndome don't appear sick, but they will lay fewer eggs, many of which are thin-shelled (and often paler in shell color.)  The birds will have to be culled from the flock.

Unfortunately, it looks like our problem hen is going to have to go.  I'll give her a week of R&R just on the off chance she needed a break, then she'll fill our bellies.