See the screen capture attached for details. The upper set of DFFs, etc., were what I wanted to copy. The lower set of DFFs, etc., are how it copied them.
The connections were present in the original. For some reason, the copy/paste moved all of the wires to the left by 1/2 grid unit, so the input sides of each of the components were disconnected and the output sides had these short additional wire stubs inside the component outlines. Cleaning all of those and reconnecting all of the inputs would have taken as much time as redrawing the schematic segment. My workaround was to copy only the components and then redraw the wires. Annoying.