Toilet rough-in space is often misunderstood. Due to the floor joist spacing, it is not always possible for the rough-in to be made to an exact measure. Even though yours measures 12-7/16", it is still technically a 12". I have 2 Toto 12" toilets that set on rough-ins that are exactly 12", and they both have a couple of inches behind the tank. Toilets are classified as being a 10", 12", or 14", but few, if any, measure exactly to their rated size. They usually actually require slightly less than their rated size such as my Totos. What I am getting at is you need to us a 12" rough-in toilet. The Toto Unifit will not help in this situation, although a 12" Unifit would work with one of the toilets designed to use that adapter.