Hiding the main search form does work to hide the main Search form, unfortunately... that doesn't solve the issue since that's the one we want to keep (so it's shown on all pages). The issue only seems to happen (i.e. showing the Search form within the Text section) when using the "Stacked Featured & Popular" layout (of course, the one we want to use), in all other layouts, the Search form within the Text section is gone.
I can PM a pic if that helps.