The 77 and later K only fit earlier bikes if you change the seat as well due to length changes, never tried an F tank on anything else so cant comment
All 500/550 frames are the same at the seat hinges and the tank mounting points - so any 500/550 tank will fit any frame, but an F or 77/78 K tank will need to be used with an F or 77/78 K seat where the seat hinge mounting points are moved forward a little to set the seat rearward enough to accommodate the larger tank.
Using an F or 77/78 K seat with an earlier model tank leaves a gap between them.
Also for F's and 77/78 K's, only the right grab rail that goes with the seat will fit.
John
edit - to be clear, the F seat is a shorter/different shape at the rear and the F grab rail follows that shape closely, so a 77/78 K seat would be pushed into the grab rail if used with an F grab rail - the other way round leaves a big space between the seat back and the rail, which looks like what you have there...