Could you possibly revisit this idea?
99% of the time the processing device in question (my Android phone) is connected to my WiFi, which also happens to be the same network that my Home Assistant server is running on.
With Home Assistant Cloud even external access is not only easy, but also rather secure since for that you don't even need to open ports in your network (which is utterly fantastic!).
Things can connect to my instance through the cloud without any fussing in the router thanks to it and I've already connected SmartThings, which runs over the internet in such a way, but also plenty of local items that aren't internet-aware themselves.
It's completely open.