If I understood correctly the question was what will be more expensive:
creating a single stargate from Syndesia to Arboreus
creating two stargates, one from Syndesia to Tartaros, then second one from Tartaros to Arboreus
Imho, you need to remember that "shortcut" you are talking about still requires you to actually travel to Tartaros, so that's an extra stargate you have to build.
Imo, stargate from one world will cost equal amount of currency (effort), regardless of where you want to travel to.
So if you are on Syndesia and you want to go somewhere, you will equally pay to construct (use) the door either to Arboreus or to Tartaros. Same goes for other worlds.
So there will be no "shortcuts".