I would also agree that it more closely fits the "association" we have with G and Georgia but J1/J2 in Georgia might be just as high overall.
Additionally, what makes the arrival of the PIE invaders unique in the context of Europe was not just the Ancient North Eurasian but also the Caucasus Hunter Gatherer which was itself different from but from the same source as G2a aka Anatolian Hunter Gatherer and later Anatolian Neolithic Farmer. Had Caucasus Hunter Gatherer been G, then it would have shown as overlap and the PIE invasion would only be important for the intrusion of Ancient North Eurasian DNA and not Caucasus Hunter Gatherer because it would already be there latent by the LNA to EBA.
I do think G represents Basal Eurasian the best, however. Some argue for Caucasus Hunter Gatherer here as well but it seems to me that G represents the most modern wave of human OOA that didn't mix with Neanderthal or Denisovan.