Actually the "tri" in triangulate comes from earth's position relative to the sun, at least when it comes to measuring distances to stars.
That's not where the tri comes from. The problem of finding the distance to a star is completely different. You know what the direction to the star is, you simply don't know how far it is. In the case of this experiment, I'm not even convinced we know where to look, and that's the problem I was trying to formulate.
The experiment on gravitational waves relies on very tight temporal constraints that do not exist when you want to know the distance to a star. And if we try to look at a recurring event with the same device, you'd have to figure out what to listen to, 6 months later. My understanding is that we roughly know how a binary system sounds like, but I don't think we can tell them apart. For that you need to at least have an idea of where it is when you do the experiment at a given time.
It's very similar to how your brain has to take two audio inputs and figure out where the sounds are coming from. To achieve this you need to be able to categorize the sounds first and infer the position for every sound separately afterwards.