By high G I’m assuming you mean second octave G right? The one we play with the regular G fingering and not the one above the highest F.
So, I remember many years ago when I was studying with a great sax teacher, I was having troubles with this G as well. We happened to be at his saxophone retreat camp with many of his students…it was really cool. Anyway, he told me to go find a spot on that hill over there in this meadow and play that G note for a couple of hours. Only the G I asked? Ya, only play that one note for at least 2 hours he said. Hit it this way, hit it that way, less mouthpiece, more mouthpiece, more air, less air, open your throat more, close your throat more, etc…every time you play it, you’ll notice something slightly different. Learn from that small thing, whether good or bad and learn from it.
Guess what? A couple hours later I could play that G really really well.