Could the red color in solution be a polysulfide? The ICP results show >10% sulfur, and polysulfides in solution have that same rich orange-red color. See, for example, NileRed dissolving sulfur, making an (alkaline) polysulfide solution:
If the red color is polysulfides, then the precipitate could just be sulfur, which crystallizes out of some polysulfide solutions.
This is 100% theory. Has anybody dissolved pyrites in aqua regia and gotten a similar result?