Best I can suggest is editing the tab descriptions (if custom tabs created in tab management) or using delimiter fields (set not to display on profile). Neither of these solutions would be much helpful for SOME tabs created by plugins as they'd need to be designed to render the description.

As for a button you could create a new tab with the display as "Button with Sticky overlay" then add a delimiter field to that tab. Once clicked would display your delimiter (custom HTML, etc..).

But what about ABOVE the tabs, or underneath the photos or page title... Could there be room there for a little introduction or help text?

For this you'd need to create a new tab in a position above or same position as the tab you want to add text above ensuring the tab is configured to raw display without title. Once done you can add a delimiter field to that tab with your intro text.