Hello!
My object is a bit rotated and I use L.Sym(local symmetry) to get my details right. The details look symmetrical near the center of the mesh but when I move towards the edges of the object, the symmetry breaks. Maybe there is a magic setting for the brush to maintain the symmetry?
Your base shapes dont look symmetrical so I am not sure why you want to use symmetry. You can resym a tool through the deform menu. Local symmetry uses the center of the mesh as a deform point, like if you were resizing two hands of a character, using local symmetry allows you to resize the meshes from their centers, not from the center of the viewport. Even if a symmetrical form is out of symmetry you can use the unify button under the deform menu in the tools menu to align it properly but this also rescales the tool so afterwards you usually have to resize it to make it fit with your model again.