Well... the context-menu 'intersect' often works on selected edges/faces ?
If that fails try to over-draw on the problem edges - that can jolt them into intersecting.
Or try grouping everything and exploding it, which also helps re-intersect sometimes...
Sometimes awkward geometry needs the faces to be subdivide using diagonals to triangulate that face and force other edges to intersect properly, once the face is divided the unwanted extra dividing lines can be erased...
Because your form is symmetrical why not divide it in half and erase the least correct part?
THEN fix the remainder... then copy that to one side and use Flip or Scale -1 on it to Flip it, then move the parts together and erase any unneeded central lines...
