I have the exact same problem - AND I HAD MY IPHONE 7 REPLACED TODAY WITH A NEW IPHONE 7 AND THE PROBLEM IS STILL HAPPENING WITH MY NEW PHONE!!! When I started using my new phone, I did not use old data from an icloud backup (in case it was a software issue from my previous phone) so I started totally fresh. I already had the SIM card replaced.
So none of these work:
1. Replacing old IPHONE 7 with new IPHONE 7.
2. Getting a new SIM card.
I also have Verizon. My husband has an iphone 6s and it works perfectly when it is directly next to my phone that has no service. So its not a coverage issue. Its something with the iphone 7.
Apple has told me that after replacing my phone if I still had a problem its no longer their problem but Verizon's problem. I know Verizon is going to kick it back to Apple. So, I think I'm going to replace my iphone 7 with an iphone 6s. Its just not worth it!