Sculpt with "Flipped" Symmetry?
I think @Spyndel’s method is better but perhaps try this. Make a copy, rotate by 180deg (in Z in your image), move over so the objects are symmetrical acoss X and sculpt with X symmetry. Strokes will be replicated on both. When done rotate the duplicate by -180deg, move overtop of the original and project the details. Hope that makes sense.