SOLVED. It took several weeks beyond when I asked the above question to solve this. There were other, strange issues too. For example, all of my content disappeared when viewed through File station, though I could see it via ssh.

QNAP remote support was very good. They were fine working with my schedule of availability so it could be worked on via TeamViewer, and I learned a couple things. The final breakthrough when they saw something in the logs that looked strange, they conferred and the guy said that it might be a RAM memory issue. I tested the RAM as per the qnap page they directed me to and sure enough it was (very!) bad. I replaced the bad RAM with the original 4 GB ram chip, did the re-syncing etc. and all problems disappeared!

I bought and installed this 16 GB RAM kit a month ago and have been happily, albeit cautiously, enjoying the "everything running smoothly" state.