I suggest you start by deciding the range you are going to shoot at. As ranges get longer, wind drift becomes a bigger problem than elevation (range estimation). If wind drift is an issue, you need a longer bullet with a better BC.
I have shot ground hogs at 400 yards, but have never shot golphers. I can recall my father shooting them with a 22 at about 150 yards max. With a 223, those little guys would be a good challenge out to 300 yards.
For 300 yards I would want at least a 69 gr match bullet. beyond that I would want a 75 or 80 gr bullet.
69 works well with 1:9. For 75 & 80 a 1:8 is required. (I have used the Sierra 80 MK in a 1:9, but it was not a short barrel, as specified by the OP)