Lead Developer
You’ll want to set it up so the site header is hidden (.site-header {display:none;}).
Then add a menu logo to the regular menu (Customize > Menu Plus > Sticky Menu).
Set the sticky menu effect to none.
Then set a taller than usual menu item in “Customize > Element Spacing”.
Once that’s done let me know and I’ll see if I can come up with the transition into the smaller sticky menu.