What options do I have to rotate a horizontal 2-gang switch box?
Your plan ain't gonna happen.  There's no way to do that.   I realize from your perspective it seems obvious that somebody ought to make "kit" for that, but they don't. Nobody installs junction boxes sideways like that. 

Since you won't turn the box, you are married to this sideways arrangement.   That's OK, it may still work out. 

Your particular line of switches, there, is called Despard which is largely obsolete.  The problem with Despard is they use bizarre and largely unobtanium switch plate covers.  And part of the problem with their covers is they don't have a good answer when you use fewer than all three voids, or all six in your case.  For instance I have a 2-gang switch plate with 3 switch positions populated (out of 6). They improvised the cover plate by wrapping a 6-hole cover plate with wallpaper.  You don't have much other choice, you can't leave empty holes for curious fingers to explore! 

However, the market has plenty of dual switches which use either the common "dual oval receptacle" cover, or the "Decora style" rectangular cover.  They even have a few triple switches in Decora, in case you want to just have switches 1-2-3 in the first rank, and nothing in the second.  That may be the option for you.



Note that all double/triple switches on the market have the throw going sideways.  That means in your sideways box, the throw would be up and down.  Which would validate the designer's original vision after all. 

You realize, of course, that a single switch throws nominally "up and down", so in your application would result in a sideways single.