Thanks, Mark. I got it figured out; those unnaturally straight lines were the culprit. They are underground pipes, and not useful for my purpose. Weirdly, though, before I asked for input, I removed them and tried running the workflow, but I got the same weird behavior. So, I decided to try again; I removed those underground pipes again, saved, closed out of all Esri products, ended all Esri processes still running in Task Manager, and then ran my workflow again (I've a script that runs the ArcHydro tools I need sequentially). Of course, it worked then.
The things you suggested are going in my back pocket, for when something else doesn't work. Especially the "Data Management Terrain Preprocessing." I didn't know that this existed. Since everything is set in our script, I don't have to worry about this. But, often, the script doesn't work (spontaneously--it's great fun when this happens), and I have to run things individually. It may be helpful to set these!
Thanks again.