I can't figure out why there hasn't been a Chu'unthor trilogy yet. I mean, how cool would that be?

I like your theory! Maybe in addition to the academy ships, the Order had an embassy or office on Coruscant for the last few centuries, since it is the capital. They could let the Republic know what they were up to from here, and coordinate efforts when needed. When Palpatine (and I love this connection - it fits his plans perfectly) suggested moving all the Jedi to Coruscant, either he used the embassy as an example of why it wouldn't be such a big change, or they actually added onto the building to construct the Temple.