AJE makes a K member for LSx engines into an S197.
2005-2014 Mustang Universal Engine Mount K-Member | AJE Suspensions
Not much else is out there that I can find. The S197 platform has decent engine options for a Ford in a LONG time. So most people simply don't mess with LSx swapping.
The wiring could be a nightmare if you plan on trying to retain as much OE Ford stuff as possible.
It sounds like your current Mustang is well sorted out, why mess with it? No need to go into the advantages of the LSx vs Modular, I am well aware of them as a long time LSx owner. I just don't see this being feasible.
My opinion, if you aren't liking the current setup on your Mustang, sell it and buy a cheap C5, pull out the LS1, drop in the LS6, then sell LS1 engine, and part out the Fbody. You would have a MUCH better platform for well ... everything and likely have some extra money left over.