So, the thread seems kind of dead, but I said I'd post some follow-up and so I am.
I did re-enable wifi calling and had pretty good luck. Since I did that, no my more Viber or Skype messages from my wife telling me "your phone is sending me to voice mail," which is a good thing. The only exception that was this weekend while I was at home. Both my wife and a friend of mine said they were being sent to voice mail, although texts were getting through, which they typically haven't when the phone started acting up. Despite that one blip, though, I've not had the issues that I was experiencing. I still think it's software related, and not hardware. In general, the phone does *not* seem to transition well from wifi to cellular, which I suspect is part of what causes the issue.
I've noticed that putting the phone in airplane mode, waiting a few seconds and then taking it out of airplane mode seems to make thing work better. Maybe it's in my head.
Regardless, I plan to leave my phone with wifi calling enabled as it does make it better.