Basically, it is the polymer submits that are the ones to sort out... One way of sorting this out is to:
Have a hidden input type="submit" button on the form so pressing Enter would normally submit the form
Use javascript to intercept pressing Enter in the form, and handle it in the custom way, by sending a click to the polymer button, however you do that. See this link.
Well, when I say all, I am excluding when within a textarea ofc.