Is there a way to run interactive automation scripts from a custom application?
Yes, there are 2 ways of doing so.
Through the header bar
Enable the application header bar and add a new header option (+ sign).
Add an 'On click' event and choose your Automation script
Through a button component
Add a component of type 'Button', and link it with your Automation script through its 'Settings' menu via an 'On click' event. You might need the 'ReportsAndDashboardsButton' soft-launch option.
Interesting to note is that you can pass data to the script input parameters in a fixed way, or via feeds.