I am not familiar with ADT Pulse, but it sounds like you may have a zwave mesh issue. I assume the tech that came out made sure you don’t have any ghost node(s) (again assuming pulse has a way to view all the zwave devices and all of their routes, etc.)
Not saying you shouldn’t move to HE. As you can see, you will get a lot of help from the community without having to call out techs. If you do decide to move them to HE you may want to take a look at this thread.
And if you want to continue to use ADT for security and want to try to integrate it with HE do a search on ADT. There are a few discussions about integration and how people of done it.