
I have tried recreating (basically by adjusting the bezier curves manually) the shape drawing two paths, and the result was a good enough outline (one of the paths set to red to show its shape):

However what I want to obtain is a shape whose fill I can customise, and none of the options to join the two paths worked. The best I could obtain was as follows, through the Exclusion command (Combine works too, the differences are explained in the next line):

Those 4-point intersections are my problem (using Combine instead of Exclusion gives only 2 points at each intersection's top and bottom angles instead): I've tried various things to make the segments between them go away, to no avail.
It might be because it's late at night where I'm at, but I really can't put my finger on a solution. What am I doing wrong?
Thank you in advance for your help.