In my opinion, this is by far the hardest puzzle on the island, and it's only one of two or three where I needed some help when I played the game. You already made it further than I did at the time. :)
There is a fairly thorough guide on Steam for this puzzle, however it's more like an analysis of the puzzle which spoils the puzzle completely. Instead, I'll try to present the solution in a series of hints (in spoilers), in case you want to figure out the latter parts for yourself. The final solution is at the bottom of the answer, of course.
You already know this one, but in case some future reader didn't pick it up in the question: why does the line not move freely? Why are there two entry points?
So yes, this is a symmetry puzzle with an invisible second line. Have you seen symmetry puzzles with two colours and black before?
In case you're trying to figure out where you've seen pink, orange and black before, maybe have a look at the immediate environment. Are those the specific colours you should be looking for?
There is a red lamp illuminating the door. Are you familiar with the colour theory puzzles yet?
If you take red out of pink, you get blue. If you take red out of orange, you get yellow. Does that seem more familiar?
Indeed, on symmetry island we can find such puzzles with a blue and a yellow line, where the yellow line vanishes more and more. In these, the blue line picks up the blue dots, the yellow line picks up the yellow dots, and the black dots can be picked up by either line. Honestly, I think the hint with the red lamp is much harder to get than simply to make the leap "oh this is a symmetry puzzle with two different colours and black, I know what to do with these", but figuring it out does tell you which of the two lines will be the active line. On to the sounds: I'm not sure how to phrase this as a hint, but there are only two relevant sound sequences, not three. One of them is pretty hard to pick up on because it takes a long time to cycle through.
The two pitch sequences are a) the dripping water which you've correctly recognised as Low-High-Mid, and b) the creaking of the ship, which is a very slow loop of four sounds and goes Mid-Low-Mid-High. You'll find that we have two small, three medium and two big dots, so that works out. But now if there are only two sequences, we can't map them to three colours, right? What could they be mapped to instead?
Instead, each sequence corresponds to one of the lines. Hence, the black dots can be used for either sequence, and we either have orange (pink) for dripping (creaking) or the other way round. It's easy enough to figure out which is which from here.
Now that you know which line covers which sequence, it's mostly a matter of finding a symmetric path such that both lines collect the dots in the right order. Pen and paper might help here. The next spoiler block contains the final solution.
Source: the Steam guide mentioned above