Should I even bother with this, or should I dump the whole thing into the compost pile for next year?

No to the first part and yes to the second part. ;)

It is one of those "old gardener's tales" that many swear by but which research shows does nothing for the plants. Egg shells just don't break down that quickly but it makes the gardener feel better adding them.

It is based on the old belief that BER is caused by a lack of soil calcium. We now know that isn't the case but by the plant's inability to use the available calcium due to many possible stress factors. There is a good FAQ here on BER and its contributing factors.

So while it can benefit the soil next year when you add your compost, I wouldn't put lots of effort into it now.

Dave

Dave,
I sorta suspected this - this is from the same book that says "leave those shop lights on 24/7 - those tomato seedlings don't need any night time!".