Thanks, Wolfgang! Starting with a fresh profile appears to have fixed the problem, at least according the limiting testing I have done with the telescope + mount set up in my basement. (Given the current Michigan weather forecast and my travel schedule, I may not be able to image again before the end of June.)

Here is what I found:

• Whenever I am using the old profile, the meridian flip hour angle reverts back to 1° not just when I run a plate solve, but also when I take a single exposure in the focuser module. Also, when I start KStars, the hour angle always shows up as 1°.
• With the new profile (all components and optical trains identical to the old profile), the HA no longer reverts to 1° after taking an exposure in the focuser module. And when I quit and re-start KStars, the HA now retains its previous setting.