Hello, DHK.
Thank you for contacting us.  I should have replied to this yesterday, because I think it is actually siimple, not complicated as it appeared at first glance  

For whatever reason, you have now have two 
Favorites, the 
real Favorites and a 
fake Favorites.
The 
real Favorites has the "★" in Safari and its name appears in 
italics in Synkmark.   The items in your 
real Favorites appear in your 
bookmarks toolbar, which is what you call the 
horizontal bar.  (Actually I like your name better but Apple makes up the names in this world.)  In Synkmark's Help Book, we classify the 
real Favorites as a 
hard folder in Safari, because you cannot delete it.
The 
fake Favorites has the regular folder icon in Safari and its name appears in 
regular font in Synkmark.   The items in your 
fake Favorites do not appear in your 
bookmarks toolbar.  In Synkmark's Help Book, we classify such a regular, normal folder as a 
soft folder in Safari, meaning that you 
can delete it.
I think what you want is to get 
your items back into your 
horizontal bar and get rid of the 12 items which are there now.  If I have understood that correctly, here are the steps to accomplish that
 Run Synkmark.
 Expand the 
real Favorites folder.
 Select and delete the 12 items (Apple, iCloud, Yahoo, etc.) which you do not want.
 Expand the 
fake Favorites folder.
 Move all items in the 
fake Favorites folder into the 
real Favorites folder.  The easiest way to do this is to collapse all of the items by holding down the option key and clicking the disclosure triangle, then release the option key and click the disclosure triangle again, then select all of the items using a shift-click to extend the selection, then either drag and drop or use a secondary click to get the contextual menu and then 
Move to
.  (The selection steps work the same in any Mac app with a standard outline view.)
 Delete the now-empty 
fake Favorites folder.
 Click in the menu: 
File > 
Export to all.