I would install a cabinet on the wall behind the toilet then.
Even if you were to switch brands and use a 2" offset, it would still be away from the wall.
The framing could have been moved, or boxed out. You must have a 15" rough. The closet you can get would be a 14" rough toilet.
Some brands have a tank that would be perhaps 2" thicker. Some brands will shift the bowl back 2" (TOTO with 14" Unifit)