Some of the Toto toilets use an adapter on the flange that allows the whole toilet to move one way or another so it will fit at either 10, 12 (it comes with this one, the others are extra), or 14". There's normally 3/4" clearance behind the toilets when you select one of these Totos (as said, each brand will have different clearances). There are more, but some of the Totos that would work are the Vespin and the Carlyle (I have one of each in my house). Using one of these with the optional 10" Unifit adapter, you'd still have about 1/2" clearance behind the toilet.
Toto Vespin II CST474CEFG with SS114 Softclose seat.
This bowl was installed on a 13-1/2" rough-in using the 14" Unifit adapter.
The water shutoff can be as close as 5-1/2" to the left of center, unless it's higher off the floor, and then it can be even closer to center.
This shutoff had been replaced with a new 1/4 turn valve with brass nipple through the wall.
Installation was by James Love of Love Plumbing & Remodel 206-949-5683
In some of the older Seattle homes, the old toilets had been wall mounted tank toilets.
Those typically are 14" rough-in and need a flange repair to use standard closet bolt connections at the flange.
Everything is on the truck for that.
The Vespin comes with a standard 12" adapter or you can order a 10" or 14" adapter depending on your rough-in distance.