Just following up here and hopefully turning the page on this issue. I took my car up to Las Vegas to have Towbin Alfa Romeo service it, since they had recently fixed a similar problem on another forum member's car. After a lot of diagnosis (they could never reproduce the faults, go figure), we eventually decided to replace the transmission hydraulic actuator. This was based on the fault codes I had saved, the fact that replacing the actuator fixed the other car that was throwing a similar code, and also based on some back-to-back drives the dealer did with another 4C, where they noted the shift quality was worse in my car.
Happy to report that I picked the car up from the dealer and drove it back to Phoenix yesterday (~300 miles) without issue. The dealer put another ~50 miles on it to verify the repair, so I'm over 350 miles now, where previously I was seeing the fault every 5-100 miles of driving. The car also shifts MUCH better than before, with a lot less clunkiness in both manual and auto modes. I didn't realize how bad it was before, since it had been that way for the entire time I've owned it (since last Jan). So I'm very hopeful the bad actuator was the issue and I can start to enjoy this car again! I'll post back here if this same issue crops up again, but just wanted to get this info out here in case anyone else runs into a similar problem in the future.
Also, major shout out to Towbin AR, who were awesome to deal with. They had excellent communication throughout the whole process and did absolutely everything they could to diagnose the root cause before just throwing parts at the car. Their pricing was also more than fair given how many hours of diagnosis they had into it. They're by far the best AR dealer service department I've interacted with and are now pretty knowledgeable on this problem, so I would highly recommend them for anyone else on the West Coast who runs into this issue.