To me, GIR's, FIR's, there kinda so-so, i mean its good to say, oh it ended up as a GIR, but i had a GIR were i skulded a long iron and it stayed 10 feet off the ground and rolled up on the green. Should i count that, it was a piss poor shot.
Best way is to say, does it meet the following criteria, and it depends on how good you are. For me, i tend to try to rank shots like this
Driver & Long game
1) What is my shot i want to play, the visualization
2) Did the shot take that shot shape, meaning did hit play a fade when i wanted it to fade, did it draw, did the ball travel with my expectations. If not what was the miss.
1) did the ball land in the spot i want, with the trajectory i want, and did it react on the green the way i wanted.
Its these type of emperical questions i think are more valuable. because they will give you answers to how your ball flight is and overall how the round went. I've hit shots i was disgusted with and the ball ended up decent in the fairway, I rather not rank that as a FIR, with a great driver were i had to shape the shot around a slightly bending dog leg to set up for good angle into the green.
But overall, GIR's will lower your score much more than short game. Its just hierarchy. Each shot before hand is more important that the next preceeding shot. They say drive for show, but your whole hole can be demolished with a bad drive, hit it OB, your down stroke and distance. Hit it in the woods, you might have to waste a shot getting out. Miss a green, your not putting for birdie. Everything preceeding the putt is to set up the overall potential of the score on your round.
Since your HDCP is a 36, i will probably say, work on your long game most of the time, you can salvage some holes with a very good short game, but that's playing with fire. Rarely does a player get away with that.