I won’t torment you with this since you were kind enough to escalate to ADC several months ago, but since you’re curious 
what is your upload speed at the device location? And is it consistent?
I’ve never clocked less than 5Mb up at the location. The wireless signal strength on the Skybell reads 100% (and it should given the proximity to the access point). We upgraded to a UniFi Security Gateway for the router, and this device does regular WAN bandwidth tests, so we can see the 5Mb up is pretty constant (fluctuates between perhaps 4-6Mb).
As part of troubleshooting I bought a new Cradlepoint LTE modem as well as the USG router, to replace the cheap Netgear modem/router combo we had been using. Didn’t help the Skybell but improved our LTE download speed from 25Mb to 50Mb, so that’s nice at least. We also tried connecting the Skybell directly to the router to rule out the UniFi wifi access point.
In going down the rabbit hole I discovered Verizon is known to have a SIP application layer gateway on their LTE network, which can cause problems with SIP audio/video calls. Unfortunately as far as I can tell Skybell is not using SIP, and instead uses CoAP (Constrained Application Protocol) for signaling. CoAP is so new there’s not much info about using or troubleshooting it, but I wouldn’t be surprised if Verizon is unintentionally doing something to mess it up.
Last month ADC did send me a replacement Skybell HD which behaves exactly the same, so we’ve now swapped out or bypassed every piece of hardware in the path. At that point I gave up. I could probably get ADC to give me my money back even though it’s way beyond the 30 day return window, but honestly I’m just too tired to swap out the doorbell again. So I’m waiting patiently in the hope that someone will figure out the problem, or that I’ll get access to better broadband service.