When I looked briefly at the log it looked like the mount was doing a meridian flip. But there also seemed to be some weirdness in the RA values being reported by the mount as it was moving.

I have seen this sort of thing in the past, particularly when the mount has tracked past the meridian. If you run with no scope it's possible to let the mount run indefinitely and I've seen it get to the expected position having rotated through almost 360 degrees. Usually the alignment has been destroyed though. Also seen pier flips via the South pole instead of the North.

One thing in this case is that the declination is negative and perhaps that makes a difference. Perhaps the mount is trying to get to -8 deg by going the long way round, via +90, 180, 270/-90.

One thing that may help is an earlier HC firmware version. - or use the NexStar+ HC rather than the StarSense. The StarSense implements sync is a different way,

Just as an experiment, I checked the Celestron Firmware Manager, and there was an update (not currently listed in the Celestron firmware history).

Ver. 1.20.20265
Bld. Sep 22 2020

I applied the update, and did a quick check this evening. Autofocus has improved, which was nice, but I still got a crazy slew. I've attached a log file, clipped to the start of the "Slew to Target."

Based on my experience so far, using Starsense with "Sync" and not "Slew to Target" works best. The NexStar+ HC works, of course, but, owing to a disability, manual alignment is very challenging for me. As I wrote earlier, using "Sync" and then slewing again with KStars works well. I just have to be careful to avoid the "Slew to Target" option.

The ASCOM driver doesn't use the HC sync command at all for the StarSense HCs. Instead it applies an offset in the driver to do sync independently of the HC. IIRC there is something similar in the INDI Celestron GPS driver which could be used.
I'm not in a position to do any INDI development at the moment but if someone wants to have a go... The 'm' command identifies the HC type, NexStar or StarSense. If the command fails it is a NexStar.

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. 

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.