You’re right that you need internet connectivity to use any of the non ADT solutions. But on a practical note you can add a UPS to your hub and modem/router and it works for many people who don’t have ADT options. That opens up more options for you like SHM or solution like Intruder Alert and SHM Delay have entry and exit delays and many more features. You can also use your existing IRIS Keypad to arm disarm SHM and manage your lock users. You can also look at ADT Tools to see how it can supplement your hub features.
There are lots of possibilities but there are compromises and some effort that needs to go into the solutions depending on how much you want to invest time/effort to create something custom.