This isn’t really just an AA problem, it’s also a visual effect called a moire pattern, caused by the interaction of the close-to-parallel strands that happens even in analog imagery, but is often worsened in digital imagery because of the underlying pixel structure. It’s worst when the linear parts run very close to parallel with the pixels grid. It can be very hard to eliminate, but one approach might be to use strands with softer edges if at all possible. That means thicker strands and a lot of material experimentation. Not sure of this helps.