Nah, I don't think the Codex was intentionally designed this way. Let's not forget that the majority of the things on it are either not taggable (NSPs, surface sites - although I guess the bodies the latter are on are taggable) or not rare (all the planet types). It's just that GGGs are both taggable and very rare. I don't think that the developers who put the thing together hastily realised this, and that there will be tag thieves looking for the fresh new discoveries of others.
Legal? Sure. Obnoxious? Sure. But if one would then go around saying that the discovery is theirs, as if they found it first, just because they managed to sell the data (with the intent of swiping the tags) before the discoverer could, then that would just make them an arrogant liar.
Which is still legal, of course.
Anyway, moving back more on topic: I was wrong, and you can't search EDSM for more than one green gas giant entry per region. I'm not sure if there's any public database where you can, although there is the
ATEL-EDMC plugin's public database at
https://raw.githubusercontent.com/Elite-IGAU/publications/master/IGAU_Codex.csv. But GGGs are listed there are as "planetFeatures" as well. In the end, the journals don't really help a lot with finding these, if there's more than one in a region.
Looking at the map again, it looks like all the GGGs that were found in regions with more than one GGG known were found before Chapter Four and the Codex.