The 77-78 recessed cap K tanks are basically identical to the 75-78 recessed cap 550F tanks. The easiest way to put one of these on a 74-76 550K is to get a seat from a 77-78 K or any year 550F.
I haven't measure my 750F tank and compared it to the 550F tank I have in my parts stash, but I am pretty confident the 750F tank is longer than the 550F.
I'm going brat style seat. So it is safe to say that a 750F tank would be the longest and not fit. It is ~2" longer and would extend past the vertical bar on the frame.
I want a 77-78 550K or 750K gas tank because the 75' 550K tank does not look aggressive enough for me.
That is not a later 550K tank because, as I said above, the later 550K tank is identical to the 550F tank.
You are overthinking this.
If you plan to use an aftermarket seat then the length of the tank shouldn't matter. Fit whatever tank you want and then adjust the seat position to fit. If you plan to use a seat hoop like the bike in the video and a pre-made seat then install the tank you want, mock up the seat, then use that to properly position the hoop.