AppSheet. Take a look at it. One problem I see is that when you "Save" a form in AppSheet it will not trigger FormPublisher. It required (I'm assuming your triggers are set up this way) a "Submit" button rather than a "Save" button. The form doesn't publish.
I second this opinion. These are two powerful tools but they don't work together. I'd like to take my form and insert it into app sheet while using Form publisher to create my word doc template.