I found several other questions that asked similar things, but were not the exact same thing.
Ideally, in one single operation. There appears to be a straightforward way to do this if the selection happens to be Edges. From the Select Menu, I can choose Select > Select Loops > Select Loop Inner Region. However, if the selection is originally Faces, the feature breaks, removing some of the original face selections, while adding no new ones. I realize that I could make my initial selection in Edges, then choose Select Loop Inner Region, and after it creates the selection, simply use the 3 key to switch back to Faces, and that would give me the result I am after. But this means extra steps that shouldn't be necessary. It seems to me that since there is something called an edge loop, as well as something called a face loop, and also, since this Select Menu doesn't specify edges nor faces in its wording, that the feature should work with either edges or faces. But it doesn't. So what does? What works to select all inner faces of a selection of faces?