I would like to create a density plot in a 2D parameter space. However, the sample consists of distinct solutions which form lines in the parameter space such that putting everything into a matrix and using imshow is not desirable because of the pixelation artefacts (Figure 1).

I have tried to plot each distinct solution as a line with opacity set to the probability it corresponds to but the blending of the different lines does not seem to be additive (i.e. the location where all lines overlap is not black). See Figure 2.

Opacity is not additive; if you overlap two objects with opacity 0.5 you won’t get a region of black (opacity 1.0).
Additionally, the point at which all your lines overlap may be smaller than 1 pixel in size, which will allow the surrounding colors to bleed in due to antialiasing.
I think the pixelated version is the most accurate solution, unless you feel like rendering all the different intersecting regions as shapes and coloring them manually.