All's well that ends well
(knock on wood)
Let me start by saying that although another box at the top of the stairs would have its advantages, the one that is there already takes up more than half the landing and a second one could make going down (or up!) the stairs challenging -- especially for my niece who lives down there.
However, they seem to have come to some agreement. They both use the basement box -- Eddie occasionally pees in the one at the top of the stairs.
There has been NOTHING in the dining room and that is what matters most of all!
Thanks for all your advice and ---- keep your fingers crossed!