I didn't label the braids because I didn't have my normal font on that system, I've changed it now.
And yes, the alternate admiral's braids are there because of TMP. It is interesting to note that during the wardrobe test Shatner's uniform is using the admirals braids from the Technical Manual, but it was fixed for the movie. This is the type of thing I'd think that William Ware Theiss would have caught, but I don't believe he was involved after Phase II was scrapped.
I, personally, think that a modified Commodore braid using the standard braid as the upper and lower bound would have worked better than pressing three standard braids together.
Also, I note the distinction between the Lieutenant Commander in a lead role verses the full Commander. Spock and Finney are both officially Lieutenant Commanders, and I'd guess Security Chief Giotto is also. I'd bet that full Commander is a rank generally reserved for commanding a starship or an outpost. But by that same theory I also believe that the commanding officers of the 12 starships upgraded to be part of the UESPA Five Year Mission were promoted to Captain (9 of them) or Commodore (3 of them) to give them more authority while operating outside of normal Federation boundaries. And so Pike in The Cage and Kirk in WNMHGB were originally Commanders, and Kirk's promotion to Captain made him the youngest to hold that rank, even if he wasn't abnormally young to command a starship.
I labeled the Lieutenant Commander - Lead
because both Scott and McCoy could have used them in their roles on the Enterprise, but didn't.