Mathematically the G IS a problem. All of them should be a bit sharp in the partial series. This can be compensated for in the overall construction of the horn or mouthpiece, although the artisan has to be very careful. If you are in love with the instrument, there are a couple of things that you can try.
1) Schilke developed a stepped bore leadpipe to deal with this and other intonation issues. You can try other leadpipes by Osmun, Najoom and others.
2) The BachBrass (Karl Sievers) blog recommends drilling the throat of the mouthpiece out. That reduces the efficiency and makes lipping up and down easier. The intonation would be improved in your case if the throat was smaller.
3) Some players have influenced the intonation by adding weighted valve caps (the third valve weight seems to have the most effect on my Monette).
4) My personal method is to experiment with the cup and backbore of the mouthpiece. Here is some research to help point you in the right direction:
Examination of the Influence of Different Mouthpiece Forms on the Resonance Behavior of Trumpets