Debbers:
I have turned off all the show specials values in the Admin/Config/Index Listing settings.
But the specials still show up if you have an empty shopping cart.
OK, I found it! I did some poking around in the code, thinking I had exausted all the configuration options.
I noticed in the default shopping cart template that there was indeed a reference to a setting for SHOW_SHOPPING_CART_EMPTY_SPECIALS_PRODUCTS
So I poked around using the tools/developers tool kit
and searched for that as a constant name
There it was. And it's a setting under Admin/config/stock ... which was one of the few config screens I never checked. It didn't sound like it would have anything to do with what I was looking for.
Whew! No code had to be touched, no template had to be edited. I hope my little adventure saves someone else some time, too.