Actually, this should be a very simple hack for Quizo, and shouldn't need another (2nd) toolbar. Toolbars that automatically wrap into multiple rows (instead of stopping at the end of a single row with a chevron button (»)) have been around in a lot of applications, fx, the older MS Office's menu bar. Browsers also have the capability of wrapping tabs into the next line.
This tweak would be useful even if you don't use a lot of toolbar buttons and/or text…fx…whenever you use a small(ish) explorer window with a normal amount of buttons, they can still hide on the right side of the toolbar row & terminate with a chevron button (»).
I hate chevrons. Hopefully Quizo will consider making the toolbar buttons automatically wrap to the next line when the toolbar becomes too narrow to include all buttons on the same line.