OK, 8 months later, I solved the problem. 

I was preparing our Celestron mounts for solar system / eyepiece observations, and I noticed that none of the mounts were properly storing time and location. After I checked the onboard batteries and performed other failed efforts, I discovered the option to factory reset the mounts. That worked! The mounts now properly store time and location.

On a whim, I tested the "Slew to Target" method under Capture and Solve, and it worked perfectly. I mean, one-iteration perfectly. Of course, KStars has been quietly updating over the past 8 months, and so that may have contributed to the solution, but I suspect issues with the mount firmware were the real problem. 

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