I assume the burnout also applies to the fact that out of the two (or three?) routes available towards Moonrise towers only one is currently implemented.
As far as i know, none of them is implemented ... at least not yet.
At every point, when you reach the place where you would get loading ... the game ends with the same sentence "this area is not part of Early Acess yet".
The route Halsin mentioned as preffered one starts on other side of Ebony Lake ... since he specificly mentioned Dark Justicars, and in the end of cinematic you can see two statues of some guys with litteraly same armor as Shadowheart have ... i dare to say that would be best place to start looking.
The second one is indeed shadowlands, you can enther there on west part of the map, somewhere between goblin camp and hag teahouse ... that is also mentioned by Halsin, but also preffered by Minthara, since she (resp. her i dunno, friend? companion? w/e ...) can provide you safe passage.
What puzzles me tho is Githyanki Creche ... since it should be accesible in north/west part of the map, but there you enter the Shadowlands as it seems ... im really looking forward for this.
Hmm, well the underdark route works, just not the actual moonrise tower bit, technically. But you can get to the boat that takes you there.
As for the Githyanki Creche, the exit towards the mountain pass is actually a little ways back from the one that takes you to the Shadowlands. It is a bit hard to find but there is a area transition specifically labeled Mountain pass, a little ways back from where you encounter the patrol at the bridge. You can also jump up the mountain a bit there, although there is nothing there other than a chest with some meh loot.