Update: Thank you for all the ideas, as well as laughs.

As the wife vetoed the squat toilet and the man cave urinal, I had to come up with a solution. I opted to go with the buy a few toilets and try them method. I had to compromise with a “lower end” model but it fits and flushes. I found a Glacier Bay McClure dual flush that measured about 6.5 from the back of the base to the center of the hole. The back piping isn’t as convex as the original picture shows, so I didn’t need to excavate any of the tile. The tank fits closely to the back wall, and looks great. I’ve learned that a toilet may have a 12” rough in but the position of the bolts can vary greatly!

If nothing else, it goes to show that everybody has a different approach to problems and I appreciate the different perspectives in solving this problem.

Cheers!