Just my experience, but I found the tapering and taping method for splicing to work poorly. Those tiny sub strands, despite being thinner than a strand of hair, are VERY strong, and the tape method snags a lot.
I've had better results with straightening out a paper clip, then bending one end back on itself and taping that over so it doesn't snag. Then, I file the tip of the "needle" so the edges don't snag. Taper the amsteel, thread it through the loop, and splice away.