I'll check out Tony's book again - I have the 3rd and 4th editions at home - but I think you are incorrect about this.
I have a late '65 K code and an early '66 A code - and you definitely you have the single exhaust set up - rounded "FROWN" axle plate like the '66 A code - not the K code flat "SMILE" plate. Look at the plate in your photo and you will see what I mean - your plate is rounded and turns down like a frown it also has that BIG cut out in the middle - the K code plate is mostly flat and turns upward at the ends like a smile and has only 3 holes in it - no big cut out.
There are a bunch of posts in the archive on this - many with pictures.
Sorry if I'm bearing bad news - but I would look your car over carefully for major repair work, front clip replacement, or floor replacement.
My K was also raced and had very severe floor cracks in this area. The floor above the plate on my car has been replaced - BUT I made sure the resto shop used my original plate and lower floor section - even a Mustang Restoration guy with 20-25 years experience didn't know about the plate differences until I told him. He said he never looked close enough becasue he had only worked on 2-3 K codes in 20 years - and only one - MINE - that needed work in that area.
By the way - where in Georgia are you located? I'm outside Atlanta.
I'll try to email you some photos of the K code plate from my car and you'll see the difference.