>>23394743 (OP)The truth of the matter is that Tomino didn't really think too deeply on it and simply set it after because there's no particular reason to set it before. He's not trying to tell a story that leads into Turn A, he's trying to tell a new story, so he simply puts it after so he doesn't need to think about any of that.
The reason only UC is mentioned is also similarly simple. In Turn A, Tomino left all the references to previous series up to his team. The script itself still referred to everything as "Universal Century", even when images shown were of different series. Tomino using UC in G-Reco is the same, he uses it as a catch-all term for everything that happened before, including the implication of other series. But because G-Reco isn't about referencing everything in the past like Turn A, he doesn't bother to go as far as adding in all the other stuff.
As far as
>>23394773 is concerned, Tomino always changes numbers as convenient. "Turn A is 10,000 years after UC" was changed to 5000 in the movie version.