After my wife's Zoom meeting this morning, I am going to call this thread solved. She had no problems with it at all. In addition, I performed an automated ping test yesterday (a ping every minute for almost 24 hours) and got less than 0.3% packet loss.
So the issue appears to be related to the older Pace 5168 modem, although it could also be due to a bad power supply...I never had a chance to test that. Or maybe there is some weird incompatibility between the modem and my particular phone lines. I would not be surprised if you do not see any problem with modem once it is returned.
In any case, I am happy. I will ship the old modem back to Sonic today. And thanks again Dane for being involved.