iPhone 6S Verizon No Signal

I just purchased my iPhone 6S from the Apple Store on Friday evening. Since updating to iOS 9.0.1, I intermittently get periods where I have no signal reception in areas that I know I can get signal in. I have attempted to turn airplane mode on and off again to force the phone to search for a signal, but once the phone has gotten "No Signal" on the top left hand corner, the phone will not reconnect to Verizon unless I restart the phone.

I have also found that even when I have signal, it is very intermittent. I constantly get notifications that my (non-iMessage) text messages were not able to be sent and I have to retry multiple times to get them to go through. I assume these two issues are related.

Even in times where I do have signal, I'll notice that the phone seems to completely lose its connection to Verizon, I'll have 0 bars of signal, no data at all, and then it will come back at a solid 3+ bars of signal with LTE. There are other times of course when I just lose it completely (and this is when I am in the same location, aka, my house, and not moving).

I thought maybe something went wrong in the update, so I have since restored the iPhone completely using iTunes and still am consistently experiencing this issue. Any thoughts on how to solve it? Maybe I just have to wait until iOS 9.0.2 or iOS 9.1, but this seems like a pretty serious issue that people are beginning to post about.