To cull or not to cull....

The Wyandette has been laying shell-less eggs for 2 months now. I am hosting a chicken slaughter class at my house on Thursday evening, taught by an experienced member of the farm co-op.  I was planning on culling the Wyandette due to the oviduct issue.  This week, she started laying eggs with shells on them.  What the heck?!  I finally make a decision on it, then she kinda fixes herself. 

The problem is she still isn't laying completely 'normal' eggs.  They are incredibly small (peewee sized) and odd shaped. Kind of golf-ball sized, with weird bumpy ends.  Here is a picture of her egg, next to one of the normal eggs. 

So I am torn. She is still underproducing given the size of her eggs. I am worried that she will start laying shell-less eggs again. If I'm going to have to cull her anyway, I'd like to do so w/an experienced teacher (like I'll have available to me during the class).  Oi.