The issue with tabs causing the right-hand buttons to disappear appears to simply be the web gui dropping the search box and buttons down to make room for the tabs. Since it isn't either extending the banner or inverting the colors of the buttons, they end up the same color as the background. They're still there, still usable, just invisible.
Is there a way to either edit the header or banner to be larger or set the colors of the wrapped buttons? I tried changing the text color, but the tabs are tied to the header custom background color, not the header text colors. Changing header background color so the tabs aren't inverting to be the same color as the main window's background color makes them visible, but it looks terrible. Maybe there's a way to tweak the OS' wrapping behavior?