Yes, I think that what the OP is saying is that water, not being perfectly incompressible, gets a little denser with depth. There are other materials which are more incompressible and their density increases more slowly with depth. I think the question is whether anybody knows of real life examples where the density/pressure curve of a substance crosses that of seawater in a way (at a credible depth) that would allow an object to settle itself stably at a predictable depth in mid water.
You can achieve something that looks similar by ballasting an object to be neutrally buoyant, then releasing it into a strong thermocline or halocline - imagine a submarine "riding a layer".
Perhaps one answer is that it's just too simplistic to assume that compressibility is the main thing that affects seawater's density as you change depth.
A.