Problem Solved!!!
I have tried all of the possible fixes on this forum/thread... and none of them fixed them problem. I am convinced that this problem is releated to, and limited to, an early batch of S7 phones. I finally called Verizon and told them that I had already spent time with Tech Support at Samsung and Verizon, and that I just wanted them to replace the phone. The phone was already beyond the 14 day Verizon return period, but still falls under the 12 month Samsung warranty period. As such, Verizon arranged to overnight me a replacement phone. Being a Samsung warranty replacement, the phone is not necessarily a "new" phone, and may be a "refurbished" phone. I agreed to this, and received a replacement phone the next day.
I have set up the phone just as I did the previous phone... same applications and settings. And this phone works just fine!!! If you are having this problem, I suggest you contact your Provider and get a replacement phone.